The Engineering Projects

Precision and Accuracy in Physics

Hello friends, I hope you are all doing well. In this article, we can talk about the precision and accuracy of the measurement. Both of these are used to analyze errors in the measurements which can be calculated. In the era of science and modern technology, accuracy and precision are essential to depict the quality of the measurements. To measure the error in the measurement precision and accuracy techniques can be used because both are used for comprehensive measurement analysis.

To calculate or describe the random errors precision of measurement can be used but if we want to describe the systematic error, accuracy of measurements can be used. Now the details of precision and accuracy, their definition, differences, examples, and their application in different fields are given below:

Difference between precision  and accuracy:

The main differences between precision and accuracy are given below:

Relationship between the accuracy and precision:

The terms precision and accuracy are different from each other, but somehow they are related to each other. Because when we measure the object or any quantity measurement then it may be accurate but not to be precise but if we determine the periscred measurement then it not to be accurate so that why both terms are not present in the measurements at the same time.to understand the relation and the difference between the accuracy and measurement  and to improve the measurement techniques some common points are given there:

• Low precision and  high accuracy
• Low precision and  low accuracy
• High precision and high accuracy
• High precision and low accuracy

Low precision and high accuracy: 

When the measurements that we can calculate are close to the standard or true value but the measured values are not similar to each other then they have high accuracy but low precision because the measurements are not matched to each other. Some examples are given below:

• The measurement of the field which we can calculate is 80 cm, 99.90 cm, and 100.02cm but the true or standard value is 100.10 cm so the values are accurate but they can’t be precise.

• If we can calculate the length of an object and the measured value is 70.01m, 80.67m, and 90.01m, the true value is 80.67 then the all values are not precise but they are accurate. 

Low precision and low accuracy: 

The measured values that can be calculated through measurements are not close to the true value and also the set of measurements are not close to each other all the measurement values are different which means they have low precision and low accuracy. Some examples are given below: 

• The measurements of the yields are 75.00 cm, 100.00 cm, and 112.00cm but the true value is 120.00cm. These values are not close to each other and neither one value is close to the true value so that is why they have low accuracy and low precision.

• For instance, if the measurement is 95.00 cm, 106.00 cm, and 101.00cm but the true value is 105.07cm then they have both low accuracy and low precision.

High precision and high accuracy:

If the measured values that we can measure are close to the true and the standard value and the set of measurements that we can calculate are close to each other then we can say that the measurements which we can be calculated have high accuracy and also have high precision. Some examples of highly accurate and highly precise measurements are given below: 

• The measurement of the length of the cylinder is 101m, 102m, and 103m and the true or standard value or accuracy is 102m then these values are precise and close to each other and they are also accurate because the measurement is close to the true value.

• The measurement of the yield is 80cm, 82cm, 83cm, and 85cm or the true value is 83cm then they have high accuracy and high precision because the values are close to the true value and all sets of measurements are close to each other.

High precision and low accuracy: 

The measured measurements are similar or close to each other but these measurements are not close to the true or standard value. some examples of these measurements which have high precision but low accuracy are given below:

• Measurement which we can measure is 79.01, 79.02, 79.03, and 79.08 but the true value is 89.01 That is why the measured values are close to each other but they are not close to the true value so it means they have high precision but low accuracy.
• Another example is if we have measurements 56.8, 56.9, or 60 but the true value is 65.01 these measurements are close to each other but aren't close to the true value so these measurements have high precision but low accuracy.

Quantifying accuracy and precision:

The quantifying of accuracy and precision in detail are given below: 

Accuracy:

By using the numerous different statistical measures we can quantify the accuracy. The steps which are involved in quantifying the accuracy are given there:

• Root mean squared error

• Absolute error

• Mean absolute error

• Relative error

Their details are given there:

Root mean squared error(RMSE):

When we take the square roots of the average squared errors then it is known as root mean squared error. The formulas which are used for root mean squared error are given below:

                RMSE= 1ni=1n(measured valuei-true values)2

Absolute error:

Absolute errors are used to determine the difference between the true value and the measured value. The formulas which are used to determine the absolute error are given below:

                         Absolute error= measured value- true value

Mean absolute error(MAE):

In the set of measurements to calculate the average error in all the measurements mean absolute error formulas are used. The mean absolute error formula is given there: 

      MAE= 1ni=1nmeasured value- true value

Relative error:

To express the true value percentage with the absolute error we can use the relative error formula. The relative error formula is given there:

          Relative error= (absolute errortrue value) 100

Precision: 

By using the measure of variability we can quantify the precision. the steps which are included in the measure of variability are given there:

• Coefficient of variation (CV)

• Range 

• Variance 

• Standard deviation

Details of these points are given below:

Range:

Range is used to measure the difference between the maximum and the minimum values in the set of measured measurement values. The formula which can be used to measure the range is given below:

Range= Maximum value- minimum value

Standard deviation: 

By using the mean values from the set of measurements to can measure the dispersion of the measurement set. The formulas which are used in standard deviation are given below:

Standard deviation: 1n-1i=1n(measured value-mean value)2

Variance:

The square root of standard deviation is termed variance. The formula of variance is given there:

Variance= 1n-1i=1n (mmeasured value- mean value)2

Coefficient of variation: 

To express the ratio of the standard deviation we can use the formula of coefficient of variation. The formula for the coefficient of variation is given there:

Coefficient of variation: standard deviationmean value 100

Classification of accuracy and precision:

The classification of the accuracy and the precision are given below: 

Binary classification: 

To measure the statistical measurements we can use accuracy and we can use accuracy in the binary classification to determine or identify the conditions of measurements. By using the accuracy to can determine the exact ratio of the true positive or the true negative.

Types of error that affect the precision and accuracy: 

The two main types of errors that affect the precision and accuracy but these two types of error have also types two main types of errors are given below: 

• Systematic error

• Random error 

Details of these errors with their types are given there:

Systematic error: 

Systematic error is defined as an error that occurs many times due to faulty equipment or may be due to an unskilled person's measurement techniques and many other reasons. But this type of error can directly affect the measurement which can be measured and give the inefficient or bad results of the measurements. 

The sources that can cause the systematic error are given below:

• Observational errors

• Environmental errors 

• Theoretical errors

• Instrumental errors 

Observational errors:

Observational errors occur due to human mistakes. When they can read the reading and observe the reading efficiently then observational errors occur some examples are given below:

•  The reading that can be measured by a human is approximately 3.4cm but it can't observe the certainty and uncertainty within it and also can’t read the exact digits of the reading.

• When the unskilled person tries to observe the readings of very small quantities then the observational error occurs maximum because to measure the small quantities skilled person is used to observe the readings.

Environmental errors:

The error occurs due to environmental factors like temperature, humidity, and the fluctuation in the electromagnetic interference and also due to the airflow which can move instruments during the measurements. Some examples of environmental errors are given below:

• When we use the thermometer to measure the temperature changing continuously in temperature can cause errors in the measurements.

• To measure the current when we used the galvanometer the needle of the galvanometer moved again and again due to the magnetic field these fluctuations can cause errors in the measurements. 

Instrumental errors:

The error occurs due to the usage of imperfect or faulty instruments during measurements.

To measure the measurements without error firstly perfect instruments are essential because without this the measurement can't be correct when we measure anything. Some examples of instrumental errors are given below:

• To measure the length of an object a ruler can be used but the readings on the ruler are visible clearly because it can be helped to measure the exact length.

• A weight machine can be shown the weight of 2kg even if we can't put any object on it this is the instrumental error.

Theoretical error: 

Theoretical errors occur when we assume the theory model but nothing can happen in reality according to these models. Theoretical misassumptions can cause different errors in the measurement and provide the un accurate or precise results. Some examples of theoretical errors are given there:

• During physics quantities measurements the air resistance is considered negligible.

Random errors: 

These errors occur due to various small unpredictable variables and these errors can’t be controlled because they occur in all measurements due to many different small or uncontrolled able variables. Some sources which can cause the random errors are given below: 

• Environmental variability

• Instrumental vartibility

• observer variability

• Sample variability

Environmental variability:

The fluctuations that can be occurred in the environment at any time like fluctuations in the temperature. Some examples are given there:

• The flow of air can distract the measuring instrument from its place and cause errors in the reading

• Air currents can also cause errors in the measurements.

Instrumental varaitabity:

The changing that occurs in the instrument during the reading there are many different instruments present that can use the noise or changes in it during measurements. Some examples are given below:

• During measuring the current the galvanometer changing the needle again and again can cause errors in the readings or measurements.

Observer variability:

When the numerous observer measured the measurement at the same time their readings were different from each other due to sight issues and many other issues. Some examples are given below:

• When the numerous observed reading through the stopwatch and stopwatch couldn't stop at the same time slime gave them vision issues.

Sample variability:

When we can measure the same object but the different samples have changes naturally we can measure them. These natural changes can also cause errors in the measurements. Some examples are given below:

• When taking different samples of the same thing or object naturally their width or thickness can be changed then different measurements come with errors.

Improving accuracy and precision:

The accuracy and the precision can be improved if we can follow the following steps which are given there:

• For improving accuracy:

• Environmental control

• Calibration

• Instrument maintenance 

• standardization

• For improving precision:

• Training

• Environmental control

• Reptation

• Instrument quality

Application of precision and accuracy:

Application of precision and accuracy in different fields are given below:

• Scientific research

• In modern technology and sciences

• In measurements

• Healthcare fields

• Monitoring environment 

• In mathematics calculations.

Conclusion:

Precision and accuracy both play vital roles in measurements because in modern physics scientists can measure very small quantities and these quantities of measurement can be accurate without error due to the accuracy and precision. Both terms are the fundamental p[art of measurement in the analysis of comprehensive measurement. 

Precise and accurate measurements provide the quality of the measurements because without these terms in measurements, too many errors occur and they are not precise and accurate.

Significant Figures - Definition, Rules, Examples & Problems

Hi everyone, I hope you are doing well. Today in this post we can discuss significant figures. Significant figures can be evolved and traced a few hundred years ago and they can be developed from time to time according to the precise calculations that can be done in mathematics and modern science and technology.

The origin of significant figures can be traced to ancient times in Greece, Egypt, or many other countries where they can be used as Significant figures in calculations or mathematics. With time these significant figures can be used by astronomers, mathematicians, and scientists as well. To measure accurate and precise measurements they can use significant figures with scientific notation. In modern physics and mathematics, significant figures can be used essentially.

Now we can start our detailed discussion about significant figures and their definition, rules, examples, and problems in detail.

What are significant figures?

Details of significant figures are given below:

Definition: 

Significant figures can be defined as:

"In the number or calculated value the specific digits which provide precision and accuracy and also impart and convey the necessity of digits in the calculated measurement."

Significant figures include the zero or the nonzero digits. Significant figures are also known as significant digits and sig figs. When we make measurements or calculate the measurement such as when we measure length, pressure, and volume and the measured value is large then we can use significant or scientific notation method. or the most capable digits are estimated and called significant figures. 

Such as if we measure the volume of a cylinder and the measurement is approximately equal to 3.97L and the uncertainty is approximately equals to 0.04L. The actual volume of this cylinder is approximately between 3.93L and 1.01L, but we can't know the certain digits in this measurement completely. But all of these three figures are called significant figures.

Additionally, the value 345.0 has only 3 significant figures 3,4, and 5 the o digit is not termed as a significant figure because it is only a placeholder.

Types of digits: 

Some digits are not to be considered as a significant figure. So the types of digits that can't be considered significant figures are given below:

• Spurious

• Leading zero 

• Trailing zero 

Trailing Zero:

The zero can only be present in the value or measurement as a placeholder. For example 1800 the last two zeros were only a placeholder but we can write the scientific notation we can raise the power of ten but in significant value, we only estimate and choose the figures that can provide accurate and precise measurement.

Leading zero:

The zero which can be present at the start of measurement and the value is known as leading zero. For instance, 00367 the first two zeros (00) known as leading zero and it can’t be a significant figure in this value 3,6, and 7 are the significant figures. Another example is 0.00456089 in this value the leading zero is not a significant figure but the zero which is present in between the digits like 6,0,8 and 9 is referred to as a significant figure.

Spurious:

Spurious digits are those when we do calculations on the instruments then the high-resolution measurement results precisions and the accuracy digits are known as spurious digits.

Another example is if the zero is present in the value after the decimal it can be considered a significant figure like 12.00 then these two zeros are also significant figures and in this value, the total no of significant figures is 4 but if the decimal is not present like 12300 then the last two zero is not considered as significant figure and in this value, the total significant digits are 5. After the decimal point, the zero is also considered as the significant figure for example 1.000 the last trailing zeros are also the significant figures and the total significant figures in this value is 4. But if the decimal is not present like 1000 then this value has only one significant figure and trailing zeros are only a placeholder.

Examples of significant figures:

Some examples of significant figures are given below: 

• 123790: All digits in this value are known as significant figures.

• 0.0056:in these digits the leading zero is not a significant figure the last two 5,6 are significant figures.

• 34986097: all digits are significant figures and the zero which is present inside them like 6,0,9,7 all are significant figures.

• 1001: all digits are the significant figures.

Rules for determining Significant figures: 

To identify the significant figures from the measurement and for the value, there are some rules. The rules that can help to identify the significant figures are given below:

• Non-zero digits in the measurement are  to be significant 

• Between the two significant digits, the zero is also a significant figure.

• Starting, leading zeros are not a significant figure. 

• Zero after the decimal point on the right side can also be a significant figure.

• Trailing zero without the decimal point is not significant. 

Nonzero digits in the measurement are significant figures: 

All non-zero digits in the measurement or the value are significant figures some examples are given below:

• 9144 all the digits in this value are significant. So the total significant digits is 4.

• 1.5678 all the digits after decimal or before decimal are considered as significant figures and the total significant digits in it is 5.

• 568.9 these all digits are significant figures. 

Between the two significant digits, zero is also considered a significant digit: 

The digit zero is not to be considered to be significant but in between the two the significant digit zero also becomes a significant digit some examples are given below:

• 10054 in this value all digits including zero are referred to as significant figures. 

• 102.60809 these all digits are considered significant figures the zeros after the decimal point are also considered significant figures.

• 101.101 in this value all digits are also considered as the significant digits or figures.

Leading zero, and starting zero are not considered significant figures:

The starting or the leading zero is not considered to be a significant figure it can only considered as a placeholder some examples are given below:

• 000102 in this value last 3 digits 1,0and 2 are called significant but the starting three zeros are not considered to be significant but it is only placeholder or leading zeros.

• 0.065 the last two digits 6 and 5 are sig figs but the starting zero or zero after the decimal point is not considered a significant figure.

Trailing zero, zero after the decimal point is considered a significant figure: 

The trailing zero, the zero on the right side after the decimal point can considered a significant figure. Some examples are given below:

• 1.89900 these all digits are considered to be significant digits. In this value, the digits 1,8,9,9,0,0 all are significant figures including the trailing zeros.

• 0.1200 in this value 4 digits are called significant figure 1,2,0 and 0 are significant figures which are trailing zeros but the first leading zero is not considered as the significant figure.

Trailing zero without a decimal point is considered a non-significant digit: 

The trailing zeros without the decimal point are not considered as a significant figure. some examples are given below: 

•  19900 the first 3 digits 1,9 and 9 are considered as the significant digits but the last trailing zeros are not to be considered as the significant figure.

• 1096800 in this value the first 5 digits are considered to be significant but the last trailing zeros are not a significant digit or a figure.

Rounding rules for significant figures:

The rounding-off technique can be used in mathematics in all calculations. In this technique the last digit if it is greater than 5 then it can be added to the previous number. for representing the rounding off number we can use n. To round the significant digit with n there are some rules which are given below:

• In the measurement value if the last digit is greater or equal to the 5 then we can +1 inti the previous digit. For instance, 1.345 then after rounding the digit the new value is 1.35 and it has 3 significant figures now.

Another example is if we have 5 significant figures like 5.9867 then after rounding off the last digit the new value is 5.987 and they have only four digits in it. 

• Now if we have the last digit less than 5 then it can’t  be added to the previous number some examples are given below:

       1.563 the last digit is less than 5 so it can’t added 1 to the previous digit and the significant figure in this value is 4. Another example is that 67.91 has the 4 significant figures and they can’t be changed because the last digit value can’t be added.

Numerical value formula:

To calculate the numerical value of significant figures for nonzero significant figure x and for the precision and accuracy p we can use the formula which is given below: 

         10n. Round (x10n) 

Where the n is equal to,

             n=[log 10(x)]+1-p

Precision and accuracy in measurements:

In the measurements precision and accuracy, both are essential. Generally, we can use precision for the stability of the measurements with repeated values and the accuracy used for the closeness to the actual and accurate measurement of the thing and the object. but with time in modern technology and science, both precision and accuracy are termed for trueness or the most closeness exact value of the measurements.  In the scientific community, the accuracy and precise measurement of the object is essential because without accuracy the measurements and problems become more complicated That is why accuracy and precision both are essential for measurements.

Addition and subtraction:

In addition and subtraction, the result of measurements can calculated with the same decimal point before and after the addition and subtraction for example:

12.56+ 0.5=13.1 they have the 3 significant figures in it another example is that

67.9+9 =76.9 and the significant figure in it is 3.

Multiplication and division: 

The result that can be taken from measurement and the result after division and multiplication of values both have the same significant figures some examples are given below: 

4.56 1.4 = 6.384 and we should rounded to 6.4 then they have 2 significant figures like before the division. another example is that 2.44 then it is equal to 9.6 they have also 2 significant digits like before the multiplication or division.

Certainty in significant figures:

In the measurement, certainty means that we confidently know the significant digit in the measurements. This known digit conveys and provides the precision of measurement and is also considered reliable because accuracy and precision are very essential in the measurements.

For example, if we can measure the length of an object with a ruler that has a millimeter marking and the measurement is equal to 24.87 then the digits 2,4,8, and 7 are certain because measurement tools can provide precise and accurate measurements.

Uncertainty in the significant figures:

Rather uncertainty in the significant figures means that which measurements we can take are not precise and accurate and we have doubts about them. When an unskilled person or limited measurement tool is used for measurement then chances of uncertainty increase because a skilled person can take accurate and precise measurements of the object and the high precision measurement tool is also needed. 

For example, if we can measure the length and the measurement is 24.56 then the last digit 6 creates uncertainty because it can be rounded off and the original length can't be measured precisely and efficiently. So that's if we want to remove uncertainty then we again measure the length and then determine the significant figures in it.

Examples of significant figures:

Some examples of significant figures are given below: 

1. 406.62 all digits in this are significant figures and the total significant figures is 5.

2. 0.00034 the last two digits are signification figures and the starting zeros are leading zeros.

3. 12090 all are significant figures and the last zero is only a placeholder.

4. 74.0 the zero after decimal is also a significant figure the total significant figure is 3. 

5. 67.08 in this all digits are significant figures and the total is 4.

These are some common examples of significant figures.

Practical problems and their solutions: 

Some practical problems to understand the significant figures are given below:

Problem no 1: Identify the significant figurae: 

Identify the significant figures in the given problems: 

1. 7696

2. 0.0074

3. 690.00

4. 60.09

5. 74.0

Solution: 

Solutions to these problems are given below:

1. All 4 digits are significant figures.

2. Leading zeros are not significant digits but the last 2 digits 7 and 4 are significant.

3. All 5 digits including zero after decimal are also considered significant digits.

4. 6,0,0 and 9 all digits are considered significant figures.

5. 7 and 4 including trailing zero after the decimal are also considered significant figures. 

Problem no 2: Calculations for significant figures:

The calculation to determine or calculate the significant figures some problems are given below:

1. 26.7+ 8.1

2. 62.4 0.04

3. 2.4+ 9.2

4. 58.0+ 4.5

5. 0.056/0.0007

Solutions:

     The solution to these problems is given below:

1.  34.8 in this value 3, 4, and 8 are significant figures.

2. 2.496 in this value 4 significant digits are present.

3. 11.6 in this solution all digits are considered significant figures.

4. 62.5 in this solution of a problem all digits are significant digits.

5. 80 are the solution and both are significant figures. 

Problem no 3: Combined operations: 

To determine the significant figures, perform the following operations:

1. (2.7+ 4) 7.9

2. (5.6 8.9) + 8

Solution:

Solutions to these problems are given below:

1. (6.7) x 7.9

=52.93 In this solution, all 4 digits are significant figures.

2.  (49.84) + 8

= 57.84 In this solution, all 4 digits are significant figures.

Scientific Notation - Definition, Rules, Examples & Problems

Hi friends, I hope you all are well. In this post, we will talk about scientific notation. Scientific notation is an essential tool that scientists and engineers can use. Archemdies presented the idea of scientific notation in the 3rd century BC. His work and scientific notation ideas are based on the novel of time, known as place value.

Scientific notation ideas have evolved over many centuries but are finally represented by Archimedes. In the 16th or 17th century, mathematicians continued to adopt changes in them and invent many other new notable contributions like Rene Descartes who developed algebraic notation. Scientific notation is a way in which we can express large number values in short form in the form of an exponent or a decimal form.

Scientific notation not only simplifies the equation, but it can also help scientists and engineers to do calculations easily. In the United Kingdom scientific notation is also known as standard form or standard index form. Scientific notation is commonly used by scientists and on scientific calculators it is referred to as “SCI” display mode.

What is scientific notation?

Scientific notation in detail is given below: 

Definition:

Scientific notation is defined as:

"it is the simplest way to express the large number into the small number or into in decimal form."

It can used by scientists, mathematicians, and or engineers to simplify the calculation and express the calculation in a very efficient way. In scientific notation, the number is expressed in the product form and they have two factors.

• A coefficient
• A power of ten

Generally, the scientific notation is written in:

                N=m 10n

There:

• N is the number
• The coefficient is m. It is equal to 1 or less than 10.
• The integer exponent is n.

Example: 

Some examples of scientific notation are given below: 

• Covert 89,700 to scientific notation.

1. Firstly move the decimal to get 8.79

2. The decimal moved 3 places to the left, then the exponent is 8.

3. Then the scientific notation is 8.79103

• Convert 0.0000023 into scientific notation:

1. Firstly move the decimal to get 2.3.

2. The decimal moved 6 places, then the exponent is 2.

3. Then the scientific notation is 2.3106.

Normalized notation: 

We can write any real number equation in the form of m10n in various ways. In the normalized scientific notation, the value of m is 1 or greater than 1 but it is always less than 10 and the value of n depends upon the larger value or decimal place. thus equation 550 can be written as 5.50102. this scientific notation helps to compare the number easily in an efficient way if the exponent value is large that means that the number is normalized as compared to smaller exponents. The order of magnitude can be assumed when we subtract the exponent by separating the numbers.in the table of logarithms, we can use this form of numbers to solve the log questions. The exponent in the normalized equation is negative if the value ranges between 0 and 1 for example: 00.6 then it can be written in 610-2. the exponents may be equal to 10 if the real number value is large like 0.0000000009 then it can be written as 910-10.

In many fields, typically or generally normalized equation is used to express large numbers of values into simple and efficient decimal form. Exponential notation is also referred to as normalized notation. But in different fields, unnormalized or simple notation or equations can be used. Generally, the latter term of notation is more used where the value of m is not suppressed in the range between 1 to 10 and the base of the exponent may be changed or other than the 10.

E notation: 

Generally, calculators or computer programs use small or large number values to present scientific notation or in some calculators, all the numbers are present or configured uniformly. 

The capital letter “E” or the small letter “e: can be used to represent or express the exponent which means “ten raised to the power of”. Typically in all computers or programs scientific notation or normalized notation can be abberived or represented in different styles. But the equation men is the scientific notation like m is the coefficient and the e is base 10 or n is for the exponent and it can be written as men or m10n. For example, 1.000 can be written as 1103 or also written as 1e3.

Engineering notation:

On the scientific calculator, the engineering notation can be written or expressed as “ENG”. The engineering notation is different from normalized notation because the value of exponent n is suppressed in normalized notation. Thus the value of m ranges in 1 ≤ |m| < 1000, other than 1 ≤ |m| < 10. So that's why sometimes the engineering notation is also known as scientific notation.

In engineering notation, the exponent value can be orally read by using prefixes such as nano, pico, Giga, and others. For example, 14.510-9 can as read as fourteen-point-five nanometers and can also be written as 14.5nm.

Significant figures:

The number of digits in the value is used to find the degree of accuracy and precision in a value. 

Significant figures include all nonzeros or zero digits but the first and the last zero digits are not significant figures if zero is present in between the numbers like 1,2,3,4,5 and so on then it is also called a significant figure. Some examples are given below:

• 456709800 In this value 7 significant figures are present and at the last two zero is only a placeholder and not referred to as significant figures.

• Then 008809 in these values there are 4 significant figures present and the starting first two zeros are not called significant figures.

So when we convert 123459900 values into normalized or scientific notation then all significant figures are present and the nonsignificant figure is removed as 123459900 has 7 significant figures then it can be written in scientific notation as 1.234599108 or also written as 1.23459900108. thus the advantage of scientific notation is to signify the significant figures efficiently.

Estimated final digit:

In scientific measurement, it is essential to record or measure all known digits from the measurement which can be calculated, and then estimate one or more digits if any information about this digit is acquirable. The estimated digits provided more information and became a significant figure because the estimated digits can provide more accurate and precise information about the leading and the ending digits.

The information that we can take from the estimated digit can help in the notation. This information also helps to choose the final digits or digits that are present in the value. For example, the estimated mass of a proton can be equal to 1.67262192369(51)10-27 kg. But in this value, the error occurs when we estimate the digit inefficiently and can be written as 5.110-37 and this estimated digit can increase the standard error or some other possible errors. 

Rules for scientific notation:

The rules that are used to convert the number into scientific notation are given below:

•  Identify the coefficient

• Determine the exponent

• Base

• Non-zero integer

• Positive or negative integer 

• Add or subtract the coefficient

• Arithmetic operation with scientific notation

Identify the coefficient:

When we move the decimal point in the value then the original number which becomes the coefficient a is taken like 230000 then the decimal moves in it and becomes 2.3 and the 2 becomes the coefficient in the scientific notation.

Determine the exponent:

Count the number of decimals that we moved in the value and this count becomes the exponent. For example: We have a value of 46000

Then it becomes, 4.6

The total no of decimals that we moved in the value is 4 then the exponent is 4 the value becomes  4.6x104.

Base:

The base of the exponent in the scientific notation is always 10.

Non-zero integer:

The exponent is always a value it is always a non-zero integer like 104 or 108.

Positive or negative integer: 

When we move the decimal from right to left then the exponent integer is positive. Example: 

                 46000 then 4.610+4

When we move from left to right then the exponent integer is negative. Example

              0.00677 then 6.7710-3

Add or subtract the coefficient:

If the exponent is the same then we simply add or subtract them. Because the same exponent can be added or subtracted and also we can multiply or divide with them. For example:

• 3.4106 + 9.7106

• The exponent is the same then we add them and then rewrite

•   3.4+9.7=10.04

• Then rewrite them into scientific notation

• 10.04106 then the new scientific notation is 

                     1.004107

Arithmetic operation with notation:

Division:

In the division method, we divide the coefficient and subtract the exponent. An example is given below:

                      81062104= 8106-42

                     =4102

Addition and subtraction: 

To add or subtract the scientific notation, the same exponent must be necessary. And adjust the equation if needed. An example is given below:

                = 2.6103+ 4.0104

 Then firstly we adjust the equation to same the exponent of both equations,

               2.6103= 0.26104

Then add or subtract them,

                   =0.26104+ 4.0104

                  =4.26104

Multiplication:

When we multiply the scientific notation then we add the exponent and multiply the coefficient.

Such as,

                 =(2104) (6102)

Then, 

                   = (26) 104+2

 So,

                 = 12108

Application of scientific notation in the real world:

Real-world applications of scientific notation in different fields are given below:

Chemistry:

Chemists use scientific notation to measure or calculate the atomic size or the atomic level. Such as Avagardo’s number which can be written scientific notation 6.0221023 which can be approximately equal to the one mole in an atom or a molecule.

Astronomy: 

In space, astronomers used scientific notation to calculate the vast distance. Because in space the distance between the moon, the sun, and other planets is vast so that's why to calculate this distance in a short or efficient way astronomers used scientific notation. For example, the distance between the Earth and the nearest star is approximately equal to 4.241013 kilometers. 

Engineers: 

Engineers work on a large scale and calculate the calculation in a very precise and efficient way so that is why they use scientific notation to express large number calculations in short form.  For example, the circumference of the earth which can calculated by engineers is 4.007107.

Physics: 

In physics, scientists can deal with very large and small quantities of measurements so that’s why to write these measurements in an efficient way they can use the scientific notation method. For example, the speed of light is 3.00108.

In education the role of scientific notation:

To become a scientist or for a scientific education understanding the scientific notation is essential. Scientific notation education starts in middle school but is explained in detail at higher levels. To become a scientist and, if we choose the engineering and technology career then the education of scientific notation is compulsory. because it helps them to calculate or, measure the very large or small measurements in a very precise or accurate form.

Challenges and misconceptions:

With the advantages and utility of scientific notation, it also becomes difficult or challenging for beginners. The common misconceptions that can be faced by beginners are given below:

• Arithmetic operations rules can't be understood or can't be used precisely. 

• Zero can be confused with exponent.

• The decimal point can't be placed properly. 

• Rules which are used for scientific notation can be misunderstood.  

Strategies that can be used to manage or overcome these misconceptions or challenges include:

• Understand the rules of scientific notation step by step and follow instructions.

• Try to solve numerous examples without help. 

• Understand the rules and solve the arithmetic operations.

Future perspectives:

With the development of modern science and technology, the use of scientific notation is also increased and it can also be improved from time to time. In modern science and technology, very large and small measurements can be calculated so that’s why the scientific notation method is used to express calculation effectively and accurately because scientific notation also helps to overcome or analyze errors in calculations. 

Examples:

                   Examples of scientific notation are given below:

• The mass of the electron is approximately equal to  0.000000000000000000000000000000910938356 kg 

But we can write in scientific notation as,

                                                 =  9.10938356×10−31

•  The circumference of the earth is approximately equal to 40000000m

    Then we can write in scientific notation as

                             =   4107

• The distance between the sun and earth is approximately equal to 149,600,000 kilometers

             In scientific notation, it can written as:

                      =1.496108

• The mass of hydrogen is approximately equal to 0.00000000000000000000000167kg

In scientific notation, it can be written as,

                           =1.6710-27

• The value 564300 can be converted into scientific notation and written as

                       =5.643105

Problems: 

Some problems are given below:

Conversion:

      Convert the following problems into scientific notation:

• 456800

• 0.005544

• 98076

• 5544320

• 0.00000000009

• 9888800000

Solutions:

             Solutions to these problems are given below:

• 4.568105 

• 5.54410-3

• 9.8076104

• 5.544320106

• 910-11

• 9.8888109

Multiplication:

                Multiplication problems are given below:

• (2108 ) (4104)

• (2.0104) (2102)

Solution:

     Solutions to these problems are given below:

• (24) 108+4

=81012

• (2.02) 104+2

=4.0106

Division:

                 Division problems are given below: 

• 5.61097.0103

• 8.41052.0102

Solution:

A solution to these problems is given below:

• 8.0105

• 4.2103

Addition and subtraction:

Perform the following operations with numbers in scientific notation:

• (5.0104)+(2.5104)

• (6103) + (4.0103)

Solution:

A solution to these problems is given below:

• 7.5104

• 6103

SI Derived Units (International System of Units)

Hello friends, I hope you are all good. In our previous lecture, we discussed the SI Base Units in detail and today, we are going to discuss the units derived from these base units. In 1960, the International Committee conference was held and they presented the measurement units that are used to measure all quantities worldwide.SI units are used to make accurate and precise measurements.

SI units are the set of seven basic units called base units and all other units are derived from these base units and called derived units. A set of seven base units is used to measure the physical quantities but derived units are used to measure the complex quantities other than physical quantities.  SI units play an essential role in modern technology and sciences.

Basic SI units: 

The basic SI units from which the other units are derived are given below:

These units are the building blocks of all others known as derived units. Derived units are the combination of these base units in the form of an algebraic combination.

Coherent derived units: 

SI-derived units which are also known as coherent-derived units are derived from base units which can be expressed in ratio, product, or exponential form. Some derived units have dimensions but some do not because their demission cancels through their ratio or product.

Derived units are used to measure the complex quantity. Derived and coherent derived units have specific names, symbols, units, and dimensions. All derived units have dimensions except steradian or radian. 22 derived units, their names, symbols, and dimensions are given below:

Applications of SI units in different fields: 

SI units are used in different fields in chemistry, kinematics, thermodynamics, photometry, kinematics, electromagnetism, or in mechanics. The details are given below:

Photometry:

Chemistry:

Kinematics:

Thermodynamics:

Importance of derived units in physics:

Derived units play a very vital role in physics and many other fields for accurate and precise measurement and also help to understand the physical phenomena. The building blocks of SI units are seven basic units by combining them the all other units derived. Derived units play an essential role in modern science and technology to measure stable and precise measurements.

The importance of derived units in physics is given below: 

• Standardization and consistency

• Efficiency in scientific computation

• Practical applications

• Simplification of complex quantities 

• Enhanced power solving

• Facilitation of understanding and communication

• Interdisciplinary relevance 

Details of the importance of derived units are given below:

Efficiency in scientific computations:

The use of derived units enhances computational efficacy in physics. Calculations involving derived units are often more straightforward than those using only base units. For instance, the 

Unit watt for power simplifies calculation ]s involving energy and time, eliminating the need for repeated conversions from base units. This efficacy is particularly important in complex calculations, simulations, and models, where reducing the number of steps can significantly impact the accuracy and speed of results.

Interdisciplinary relevance:

Derived units are not confined to physics alone but are used across various scientific disciplines, fostering interdisciplinary research and applications. For instance, the coulomb, a unit of electric charge, is crucial in both physics and chemistry. The use of common derived units across different fields facilitates collaboration and integration of knowledge, leading to achievements in areas such as materials science, biophysics, and environmental science. This interdisciplinary relevance underscores the versatility and universality of derived units in scientific inquiry.

Standardization and consistency:

One of the foremost reasons derived units are vital in their role in standardizing measurement globally. The SI system, established and maintained by the International Bureau of weights and Measures (BIPM), ensures that measurements are consistent and universally accepted. Derived units such as newton(N) for force, the joule (J )for energy, and the watt(W) for power, are constructed from base units like the kilogram(kg), meter(m), and second(s). This standardization is crucial for scientific communication, allowing researchers from different countries and disciplines to compare results and collaborate effectively on confusion or the need for conversion factors. 

Practical Applications:

In practical and industrial contexts, derived units are designed to be more user-friendly for real-world measurements. For example, the hertz(Hz) is used to measure frequency, providing a more practical and comprehensible unit than cycles per second. Similarly. The use of derived units like the lumen(lm) for luminous flix or the sievert (Sv) for radiations enables more precise and accessible measurement and regulation in various industries, including healthcare, engineering, and environmental monitoring.

Facilitation of understanding and communication:

Derived units provide a clearer and more intuitive understanding of physical phenomena. For example, energy is measured in joules, which convey specific physical meaning, more straightforwardly than its base unit equivalent. This clarity extends to educational settings, where students can grasp complex concepts more easily when they are expressed in familiar derived units. additionally, using standardized derived units in scientific literature and presentations ensures that findings are communicated effectively, fostering a shared understanding among researchers.

Simplification of complex quantities:

Many physical quantities are inherently complex and can't be conveniently expressed using only base units. Derived units simplify these expressions, making them more manageable and intuitive. For instance, pressure is commonly expressed in pascals(Pa) rather than its base unit form of kg/ms-2. This simplification is not merely a matter of convenience but also aids in understanding and interpreting physical concepts more readily. It allows scientists and engineers to work more efficiently, reducing the potential for error and misinterpretation.

Enhanced problem-solving:

Derived units play a crucial role in problem-solving by aiding in dimensional analysis, which involves checking the consistency of equations. Dimensional analysis ensures that equations are dimensionally consistent, meaning that both sides of an equation have the same units. This technique is fundamental in verifying the correctness of quotations, deriving new relationships, and identifying potential errors. For example, ensuring that the units on both sides of Newton’s second law (F=ma) match confirms that the equation is dimensionally consistent and physically meaningful.

Application of derived units: 

Some applications of derived units are given below:

Joule(J): 

This unit are used for heat, energy, and work. Their application in physics is given below:

• Mechanics: the work which is done by a person or an object can be measured in joules. This concept is also used to understand the potential and the kinetic energy.

• Thermodynamics: according to the first law of thermodynamics the energy that can be expressed in joules can't be created or can’t be destroyed and the energy in the form of heat can always be measured in joules.

• Electricity: in the electrical system the energy which can be used in the form of electricity can be measured in joules because work is also done in it.

Watt(W):

These units are used for power, their application in physics are given below: 

• Mechanical systems: the power that can be consumed in engines or different mechanical systems can be measured in watts.

• Electrical engineering: in our daily life or households like bulbs, ovens, and other electronic devices, the electric energy that can be consumed is measured in watts. 

• Thermodynamics: In cars engines, and other electronic devices which consume electrical energy can be measured in watts.

Volt(V): 

  These units are used to measure electric potential, and their application in physics is given below:

• Power distribution: the voltages that can be distributed to the power line can be measured in volts. 

• Electronics: the electrical devices like capacitors, diodes, and others that can distribute the voltages. These voltages which can be distributed are measured in volts. 

• Electric circuits: in electric circuits, the potential that can be distributed is measured in volts.

Tesla(T):

These units are used to measure the magnetic flux density, their applications in physics are given below:

• Physics research: In physics research when high magnetic fields are used then these field strengths can be measured in teslas. 

• Electromagnetism: the magnetic field strength in the magnets can be measured through teslas.

• Medical imaging: In the medical field medical devices like MRI machines have also a strong magnetic field which can also be measured in teslas.

Ohm(Ω): 

This unit is used to measure electric resistance, their applications in physics are given below:

• Thermistor: temperature-sensitive resistors use temperature and resistance both and to measure or control the temperature ohm is used.

• Circuit design: in electrical circuits where electric current is passed resistance is also present to measure the resistance we can use ohm.

• Material science: to manufacture the electronic device, an ohm is used to measure the resistance.

Henry(H):

This unit is used to measure inductance, their applications in physics are given below:

• Radiofrequency: In radio when the tune is played then the frequencies are matched because during their manufacturing frequencies are measured in hertz.

• Electrical engineering: To make inductors and coils of inductance to make a strong magnetic field Henry is used to measure the inductance.

• Power supply: to supply the power current smoothly without changing in current and voltage inductors are used.

Farad(F): 

This unit is used to measure capacitance, their applications in physics are given below:

• Energy storage: capacitors which are used in electrical devices are used to store energy and the farad is used to measure the capacitance of a capacitor. 

• Communication systems: In television, radios, and other electronic devices capacitors are used to store energy.

Newton(N):

This unit is used to measure force, their applications in physics are given below:

• Aerospace: Newton is used to find or determine the thrust and friction that are produced by engines during flight.

• Classic mechanics:  Newton is used to determine the forces that are produced by an object or a person. Newton also presented 3 laws.

• Engineering: the engineers who build the buildings and bridges calculate the forces to ensure that these can bear stress or not.

Pascal(P):

This unit is used to measure pressure, applications of Pascal are given below: 

• Engineering: The engineer used Pascal to calculate the stresses of the material and then used the material.

• Fluid dynamics: Blood pressure, atmospheric pressure, and all fluid pressure can be measured and calculated through Pascal.

• Meteorology: to measure the climate and weather Pascal is used.

Coulomb(C):

This unit is used to measure electrical charge, their application in physics are given below:

• Capacitors: capacitors are used in electrical devices to store energy and to maintain the current flow.

• Electrostatics: in the electrostatic experiments coulomb are used to measure the electric charge that flows through them.

• Batteries: in batteries, the charge stored that is used after completing the charging.

Conclusion: 

Derived units are used in various fields to measure complex quantities and physical phenomena that can't be measured by using the base quantities. Derived units like joule, watt, kelvin, coulomb, Pascal, and all others are derived from basic seven base units in the form of exponent. Now derived units are used in modern technology and sciences. Scientists used these units to measure the different quantities precisely and accurately. From time to time, the SI system can also continue to adopt the changes and present more suitable and precise units for the measurement of the quantities. The SI system adopts many changes in its units and redefines them.

SI Units(International system of units)

Hi, friends. I hope you are all well. Today we will discuss the SI ( International system of units) in detail. An international committee conference held in 1960 concurred on a set of definitions used to describe the physical quantities. This committee and the founded system are called System International (SI).

SI units are the measurement systems used generally to measure the standards.SI units play a vital role in measuring standard quantities in scientific and technological research.SI units are a set of basic 7 base units from which derived units are defined.SI units also play a vital role in modern metrology and now they become a part of the foundation of modern science and technology.SI units can be categorized into three types:

• Base units
• Supplementary units
• Derived units

Now we will discuss what SI base units are, their definitions, importance, and applications in detail.

What are SI base units?

SI base units are the basic standard units explained by an international system (SI) of units. SI base units are known as the building block of the international system of units because all other units are derived from these basic standard units.

Base units are used to express the base quantities. And the other units are used to express the derived quantities which are derived from base quantities and units. The physical quantity and units are:

These SI units were globally accepted for measurement of the physical quantities. 

The basic definition of SI base units: 

The basic definitions of the SI base units are given by the System international unit in detail below:

These definitions are the old and basic definitions but with time and with more research these definitions can be revised and new definitions of these base units are presented.

Revised and new definitions of SI base units:

In 2016 November 16 the old and basic definitions of base units can be revised but it can be effective from 2019 May 20. The redefinition of the meter can be revised by understanding the physical artifact and it is not based on the property of nature. Other basic units like candela, kilogram, mole, and ampere can be connected to the revised definition of kilogram which is presented by an international prototype of the kilogram, by storing the cylinder of platinum-iridium in a vault near Paris.

The revised and new definitions of SI base units are given below.

Application and Importance: 

Application and importance of all seven base units in detail are given below: 

Meter:(the unit of length)

• Physics and engineering: to measure the accurate length in constructing the building and in designing the machinery.

• Astronomy: to measure the distance between the objects and the measurement is precise and accurate.

• Everyday life: in our daily life meter is used to measure the length of an object and also measure the distance or the plot size.

Candela:(unit of luminous intensity)

• Lighting industry: to measure the precise and accurate luminous intensity which is important in designing and creating a lighting system.

• Cinematography and photography: to achieve the effective and desired visual effects accurate measurement of light is essential.

• Vision science: to understand or design human vision aids measurement of luminous intensity is very essential.

Second:(the unit of time)

• Synchronization: accurate and precise measurement of time is very important for clocks at the global level and also shows an impact on telecommunication and in many other social systems.

• Daily life: in daily life time measurement is essential to make a schedule and to do work on their given time.

• Physics experiment: to measure the velocity, speed, and distance time measurement is essential to do work or experiment on time.

Kilogram:(the unit of mass)

• Medical field: to make the dosages and the multivitamins the mass of a substance is essential to measure because if the mass is increased to make a low dose of medicine then it can show very adverse effects.

• Science and industry: to make the chemicals in industry accurate and precise measurement of a substance is very important. 

• Trade and commerce: for fair trading the measurement of mass is essential.

Mole:(the amount of substance)

• Environmental science: in the environment, the amount of pollutants and harmful gases can be measured through a mole.

• Chemistry: In the chemical reaction of chemistry the mole is the essential and fundamental part of a reaction or the chemistry experiment

• Pharmacology: in the pharmaceutical industry the precise and accurate measurement of mole is essential to make chemicals and medicines.

Ampere:(the unit of electric current)

• Medical equipment: many medical machines like x-ray machines, MRIs, and CT scans can measure the precise measurement of electrical current.

• Electrical engineering: to measure the precise and accurate current in electronic devices. 

• Power system: to distribute the electric current in the electrical system and to operate the power system the measurement of electric current is essential. 

Kelvin:(the unit of thermodynamic temperature)

• Industrial process: in industries to manufacture the material the accurate and precise measurement of temperature is vital.

• Climate studies: the global and climate temperature change every time and to measure the accurate temperature of climate, the temperature can be measured accurately.

• Scientific research: in physics, chemistry, and many other science subjects in which we can perform experiments, the measurement of temperature is essential to run the process of experiment. 

Interrelationship and derived units:

The foundation of all SI units in the SI system are the seven base units which are interlinked. To measure the complex and difficult physical quantities derived units are used which are a combination of seven base quantities. Some examples are given below: 

•  Watt(W): this is the unit of power and can derived from the base unit (J/s).

• Newton(N): this unit is used for force and derived from the base unit meter, seconds, and kilogram.

• Joule(J): this unit is used for energy and derived from base units like seconds, kilograms, and meters.  

These are some examples of derived units that are derived from the combination of different base quantities.  

The evolution and future of SI units: 

The SI unit's definition can be changed with time to increase precision and stability. because these units can be used in modern science and technology and also in meteorology processes.

The SI system can do more research to evolve modern technology and discover more precise and effective results of their research to make the bright future of SI units. Potential future changes could involve redefining units based on even more fundamental principles or developing new measurement techniques that further enhance precision and accessibility.

Conclusion:

The international system of units(SI) plays a vital role in physics, scientific research, pharmaceutical industries, and our daily lives. The seven base units are the fundamental and the foundation of the international system of units. These units help to measure all the quantities in a very effective and the results are precise and accurate. With time science and technology progress the si system also tries to maintain more precise and relevant changes in their research.

What is Velocity? Definition, SI Unit, Examples & Applications

Hello everyone! I hope this article will find you in great health. Today, in this article, we will discuss in detail: What is velocity? We will take a look at what exactly velocity is, how it can be measured, what scale has System International (SI) defined to measure the velocity, how many forms of velocity do exist in our surroundings, and what are the real-life applications of this physical quantity?

I will let you guys know about how velocity is a regular part of our daily lives and how it behaves in the environment we are living in. To understand the basic concept we need to have a deeper look at its real-life examples. A detailed discussion on velocity to have a better understanding is provided in the next section. Let’s get started.

What is Velocity?

An earthly object can possibly have two states i.e. rest or motion. If an object is in motion, a numerical value called Speed is used to measure how fast or slow the object is moving? Speed is defined as the distance covered per unit of time. So, if an object covers a distance of 1 meter in 1 second, its speed will be 1m/s. As speed is a scalar quantity so it just gives the scalar information(about motion) and doesn't tell us anything about the direction of the movement i.e. object is moving towards north, south or may have a circular motion.

So, in order to completely define the motion of an object, an equivalent vector quantity of speed was introduced and named Velocity. Velocity, not only gives the numerical value(speed) but also tells the direction of the moving object. In simple words, speed plus direction is equal to velocity and as speed is distance per unit time, similarly velocity is displacement per unit time.

Now let's have a look at a proper definition of Velocity:

Velocity Definition

• The velocity of an object is defined as the displacement(covered by it) per unit time in a particular direction.
• If two objects are moving in the same direction at different speeds OR in different directions at the same speed, they will have different velocities.
• Two objects will have the same velocities, only if both are moving in the same direction with the same speed.

Let's have a look at the symbol of velocity:

Velocity Symbol

• Symbols are used to represent physical quantities as writing the full name is time-consuming and sometimes overwhelming.
• The symbol used to represent Velocity is "v"(small character).
• As it's a vector quantity, so its symbol is either written in bold or with an arrowhead at the top.
• Sometimes, v(t) is also used as a velocity symbol, where t shows the time span.
• The below figure shows the velocity symbol more clearly:

Now let's have a look at the mathematical formula for calculating the velocity of an object:

Velocity Formula

• Velocity is defined as displacement per unit time, so its formula is:

Velocity = Displacement / Time

v = d/t

As v & d are both vector quantities, so written in bold while t is a scalar quantity.

• If we are calculating the average velocity of an object, the velocity formula will be:

Average Velocity = Distance Covered / Total Time

?v = ?d/?t

?v = (d2 - d1) / (t2 - t1)

where t1 & t2 are initial and final time intervals and d1 and d2 are initial and final displacements of the object.

Now, let's drive the velocity unit from its formula:

Velocity Unit (SI)

• As Velocity formula is:

Velocity = Displacement / Time

where SI unit of displacement is the meter and that of time in seconds.

• So, the SI unit of velocity is:

Velocity = meter / second

• SI unit of velocity is normally written as m/s or ms^-1.
• Other velocity units are:
  1. ft/s
  2. mph
  3. km/h etc.

In the game of cricket, the velocity of the ball is usually not measured in SI units rather they measure it in either kilometer per hour or miles per hour.

Velocity Dimensions

• Since the unit of displacement(meter) shows the quantity of length so its dimension would be “L”.
• Similarly, when it comes to the “second” it shows the amount of time so its dimension will be “T”.
• Putting these dimensions in the velocity formula, we have.

Velocity Dimension = [L/T]

v = [LT^-1]

 

Few Velocity Terms

Depending upon various factors, velocity has been divided into multiple types as discussed below. Let’s read through them all.

Negative Velocity

• If an object is moving in a coordinated plane, then its velocity is measured from some fixed reference point.
• In such cases, if the object is moving away from the reference point, its velocity is termed as Negative Velocity.

Let's understand it with an example of a ball thrown upwards:

As we know, Earth's gravitational force pulls everything towards it. So, considering the earth as a reference point, when you throw a ball in the upward direction, it's moving away from its reference point(Earth's center). So, during its upward flight, the ball will have a negative velocity and thus is written with a negative sign.

Zero Velocity

• When an object is not covering any distance with respect to the varying time, it will be said to have Zero Velocity.

Let's continue that example of the ball moving upward:

As we have seen in the previous section, the ball will have a negative velocity while moving upward. But when it will reach the maximum height and rite before moving back in the downward direction, for an instance it will have a zero velocity, as it won't be moving either upward or downward.

Positive Velocity

• If the object is moving towards the reference point of its coordinate system, its velocity is termed as Positive Velocity.

Let's add some more in that ball example:

Once the ball reaches the maximum height, it will start moving back in the downward direction. Now, the ball is moving towards its reference point(Earth's Core) so it will be said to have positive velocity now.

Initial Velocity

• As moving objects have variable velocities over different periods of time, that's why velocity is normally measured in the rate of change(?v).
• So, the first velocity of the object, when it comes under observation is termed as Initial Velocity.
• The Initial Velocity is also termed as the velocity of an object at time t = 0.
• Initial velocity is denoted in Physics by the alphabetic letter "u" or "Vi".

Let's understand it with the same example:

We have seen the ball example thrown upward. If we consider both of its loops(moving upward and then downward), its initial velocity will be right where it left the hand of the thrower. It will have a maximum initial velocity as during the upward direction it will slow down and during the downward direction, it will lose some to friction. But if we only consider the second loop i.e. the ball has reached its maximum position and now it's moving downwards. So, in this scenario, the initial velocity of the ball will be 0. I hope it got cleared.

Initial Velocity Formulas:

• Using the equation of motion, we can easily derive different mathematical expressions for the initial velocity. The first equation of motion is,

v = u + at

• If we are provided with the time, final velocity, and acceleration, we can calculate the initial velocity using the formula given below.

u = v - at

The above expression shows when we multiply acceleration with the given time and subtract this product from the final velocity, it gives us the initial velocity.

• If a scenario comes where distance, final velocity, and acceleration are provided, we can find initial velocity from a mathematical expression given below:

u² = v² - 2aS

• In case, we have only time, distance and acceleration to find out the initial velocity, we can use the formula shown below.

u = S/t - (1/2) at

• If the final velocity, time, and distance are provided in the statement, an effective way to find out the initial velocity is given below.

u = 2(S/t) - v

 

where,

• u = initial velocity.
• v = final velocity.
• a = acceleration.
• t = time consumed.
• S = distance covered.

Final Velocity

• The velocity of a body at the end of the provided time is known as the Final Velocity.
• We can also define Final Velocity as the last velocity of the object while it's under consideration.
• The final velocity is usually denoted by “v” or “V_f”.

Final Velocity Formulas

• Using the equation of motion, the final velocity can be easily calculated with the formula given below, when we are provided with the initial velocity, acceleration, and time consumed:

v = u + at

or

V_f = V_i + at

• If the statement has asked us to calculate the final velocity and provided us with distance, initial velocity, and acceleration. We can use the below formula for quick calculations.

V_f² = V_i² + 2aS

Where,

• V_f = Final Velocity.
• V_i = Initial Velocity.
• S = Distance covered.

Let's understand the concept associated with the final velocity through a visual example.

A projectile motion of the ball thrown from one end is shown in the figure below. At time zero (t = 0), when a guy in a purple shirt throws a ball, the velocity of that ball at this time is considered initial velocity. After reaching a particular height, when the ball starts moving downwards and reaches at t = 8 seconds in the hands of a guy wearing a green shirt. At t = 8 seconds, the velocity of the ball is the final velocity. After this velocity, an object comes again into the stationary position.

Similarly, if you drop a ball from a specific height and allow it to move towards the ground as shown in the figure below. The moment you drop the ball, the velocity is called initial velocity. Whereas, the moment when the ball touches the ground, the velocity will be known as the final velocity.

Now let's have a look at different types of velocity in detail:

Types of Velocity

Depending on the type of object and its motion, we have numerous types of velocities, a few of them as discussed as follows:

Average Velocity

• When an object is moving in a specific direction, the ratio between the total displacement covered and total time consumed is known as the average velocity of that particular body in motion.
• It is denoted by “v” or "Vav".
• We can also define this quantity as the average rate at which the body changes its position from one point to another point.

Average velocity = total displacement covered / total time taken

• If we take the difference between the initial and final displacements and divide it by the difference of initial and final time, it will give us average velocity in return.

?v=?x/?t

?v = (x2-x1) / (t2-t1)

Where,

• x2=final displacement
• x1=initial displacement
• t2=final time
• t1=initial time

Average velocity cannot tell us how fast or slow an object is moving in a specific interval of time and for that, we have another type of velocity called Instantaneous velocity.

Instantaneous Velocity

• The velocity of an object at a particular instant is known as the instantaneous velocity of that object.
• In other words, the velocity of a moving body at a specific point is its instantaneous velocity at that point.
• Instantaneous velocity is similar to average velocity but we need to narrow the time intervals i.e. time approaches to 0.
• It is denoted by “Vinst”.
• If any subject has a fixed velocity over a specific time period then its instantaneous and average velocity will be the same.

By applying a limit “t” approaches zero on the average velocity provides us with the instantaneous velocity as shown in the formula given below.

V_inst = Lim _{t -> 0} (?d/?t)

Take a look at the figure below, the velocity at point “p” depicts the instantaneous velocity of a moving body.

The figure below shows the relation between average and instantaneous velocity. The velocity is represented by the red line and has been divided into several segments. The position is displayed on the y-axis whereas the x-axis shows the time consumed. In the first interval, Jack has covered 3 miles in the first 6 minutes. In the second interval, Jack stopped for 9 minutes. Whereas, in the third interval, Jack covered another 5 miles in 15 minutes. If we divide the total displacement covered by Jack by the total time consumed during the whole travel, it will give us an average velocity.

Constant Velocity

• If a body is traveling at the same speed for a long time and is not changing direction, then its velocity will be considered as Constant Velocity for that particular interval of time.
• In other words, it can be said that a body will have a constant velocity if it is moving at a constant speed along the straight line. This straight line can be represented by the formula given below.

x=xo+vt

Where,

xo=position of the body at t=0

• An object can have a constant velocity if it is moving in the presence of very little or no friction. Less friction allows that object to move freely just like in ice hockey where a hockey puck slides on the ice as shown in the figure below.
• If an object is moving with a constant velocity, it will have zero acceleration because acceleration is the rate of change of velocity per unit time.

a=dv/dt=0 v=constant

This scenario can be visualized through a velocity-time graph as shown in the figure below. You can see a straight line for each time interval depicting the velocity is constant throughout with “0” acceleration.

Variable Velocity

• If the velocity of an object is changing in either direction or magnitude or both, it is said to have a Variable Velocity.
• If an object is in a motion and is covering unequal distances for every equal interval of time, we can say it is moving with a variable velocity.
• In simple words, variable velocity is a type of velocity that changes with time.

Let's understand this from a real-life example.

For instance, if a fan installed in your room is rotating at a continuous speed, its velocity will be variable because its direction gets changed every time.

Orbital Velocity

• The velocity required to make an object overcome its gravitational force and rotate within an orbit is called orbital velocity.
• The movement of satellites around the earth and the movement of stars around the sun are the best examples of orbital velocity.
• It is denoted by “Vorbit” and for Earth, its mathematical formula is:

Vorbit=GMR

Where,

• G=gravitational constant=6.6710-11m3kg-1s-2
• M= mass of the planet
• R=radius

Escape Velocity

• Escape velocity is the type of minimum velocity required for an object to escape from the gravitational force of a massive body (moon, earth, etc.) and to move out somewhere in space.
• Escape velocity increases with an increase in the mass of a body.
• It is denoted by “ve” and depends upon various parameters including the mass of the planet and radius.
• We can calculate it using the mathematical expression given below.

ve=2GMr

Where,

• G=gravitational constant.
• M=mass of the planet.
• r=radius.

Angular Velocity

• The rate of velocity at which a body rotates around a particular point or center in a given amount of time is called angular velocity.
• It can also be defined as the angular speed at which a body rotates along a specific direction.
• Angular velocity is denoted by omega “?”.

Angular Velocity Unit

• System International has assigned this quantity with a unit known as radians per second.
• This quantity can also be measured in many other units as well depending on the requirements and they include:
  1. degrees per second
  2. degrees per hour

Let's have a look at how to find the angular velocity of a moving object?

Angular Velocity Formula

To calculate this quantity, a formula is given below.

?=??/?t

Or,

?=v/r

Where,

• v=linear velocity
• r=radius
• ?=angular velocity

Conversion of Angular Velocity into Rotational Velocity

• When we measure angular velocity in either revolution per minute or rotations per unit time, it becomes rotational velocity.

The direction of motion of an object moving with angular velocity is always perpendicular to a plane of rotation. It can be measured using the right-hand rule. The whole concept is shown in the figure below.

 

Linear Velocity

• As it is very clear from the name of this quantity, when an object moves along a straight line in a single direction, its velocity will be a linear velocity.
• It is simply denoted by the alphabetic letter “v”.

The above figure shows that the linear velocity is dependent on the two different parameters i.e., distance covered and the time consumed to cover that particular distance.

Let's have a look at how to find linear velocity?

Linear Velocity Formula

It can be calculated using the below mathematical expression.

velocity=distance/time

v=S/t

As we know,

S=r?

Putting this value in the above formula we have,

v=r?/t

The linear velocity can also be represented in terms of an angular velocity as given below.

v=r?

Terminal Velocity

• A steady speed that an object achieves when falling through the liquid or gas is known as its terminal velocity.
• In other words, we can describe this quantity as the constant vertical velocity of an object.
• It can also be defined as the highest velocity maintained by a body that is falling through the liquid
• It is denoted in Physics by “vt”.

Factors Involved in Terminal Velocity

• This quantity is dependent on multiple factors e.g.,
  1. the mass of the object
  2. drag coefficient, acceleration
  3. projected area
  4. fluid density.

Terminal Velocity Formula

• Terminal velocity can be calculated using a mathematical expression given below:

vt=2mgACd

Where,

• vt=terminal velocity
• g=gravitational acceleration=9.8 ms-2
• m=falling object's mass
• Cd=drag coefficient
• A=projected area
• ?=fluid density

Uniform Velocity

• A scenario when a moving body is covering the equal displacement in equal internal in a fixed direction is said to have a uniform velocity.
• It is a stable velocity that does not change in multiple intervals of the time consumed and direction remains the same too.

Let's understand with an example.

• A motorbike traveling with a speed of 20 kilometers per hour towards the east has uniform velocity.
• Uniform velocity can be easily visualized on the distance-time graph as shown in the figure below.

Non Uniform Velocity

• A body that covers unequal displacement in equal time intervals is said to have non-uniform velocity.
• In this case, either direction of motion or both rate of motion and direction can be changed for an object in motion.

Let's understand this with a visual example.

The track of a car moving with non-uniform velocity is shown in the below figure. Unequal displacements covered in equal intervals of time can clearly be seen from the velocity-time graph.

Relative Velocity

• Relative velocity is the vector difference between the velocities of two different objects.
• It can also be defined as the velocity of an object with respect to an observer who is at rest.

Let's understand the overall scenario with an example.

For instance, the air is causing some hindrance in the airplane’s track or a boat is traveling through the river whose water is flowing at a particular rate. In such cases, to observe the complete motion of the object, we need to consider the effect of the medium affecting the motion of a moving body. By doing so, we measure the relative velocity of that moving object as well as the medium’s velocity affecting its motion

Let's have a look at another example to have a better understanding of relative velocity.

Finding Relative Velocity

• The relative velocity of an object “x” relative to the object “y” can be expressed as shown below.

Vxy=Vx-Vy

• Similarly, the relative velocity of an object “y” relative to the object “x” is given below.

Vyx=Vy-Vx

• Taking a look at the above equations, we can develop it as:

Vxy=-Vyx

• The above equation shows that both relative velocities are equal in magnitude but opposite in direction.

|Vxy|=|Vyx|

• In the first case, the observer is moving in the rightwards and the ball was thrown by a girl is moving in the same direction and the person dragging that girl is traveling in the same direction as well. Therefore, all these quantities are positive.
• In the second case, the girl is throwing the ball in opposite direction to the direction in which the observer is moving. That is why the signs of the velocities are negative for both the observer as well as the ball.

Now, let's have a look at what parameters creates a difference between speed and velocity.

Difference Between Velocity and Speed

It has been proved through various research studies that most of the time people get confused when it comes to speed and velocity. They mostly get confused in implementing their concepts separately in different scenarios as and when needed.

Basic Difference

If I tell you the very basic difference between these two quantities, they are just as different as distance and displacements are.

• Speed is the rate of change of distance with respect to the time consumed in covering that particular distance.
• Whereas, velocity is the rate of change of displacement (shortest distance) covered by a moving object in a specific direction per unit of time.

Let's have a look at some more points to understand the difference effectively.

• Speed depicts that how fast an object has the ability to move. An object at a stationary position always has zero speed. The speed needs no direction to be defined.
• It is a necessity for someone to consider the direction in which a body is moving if one is going to describe the velocity.

Therefore, keeping in mind the above points, it can be said that a direction creates a major difference between speed and velocity.

• The quantity that doesn’t require direction to be measured is known as the scalar quantity and it only needs magnitude to be defined. Therefore, speed falls into the category of scalar quantities.
• The quantities that need direction and cannot be defined without it are known as the vector quantities. Therefore, velocity belongs to the family of vector quantities.

Let's understand through an example.

For instance, 30 kilometers per hour is the speed of a moving vehicle whereas 30 kilometers per hour east shows the velocity of the same vehicle.

• It is very simple to calculate the speed of any moving object compared to calculating the velocity of the same object.
• Average speed is the ratio between distance traveled and the time taken.
• Whereas, the average velocity is the ratio between the change in position (?S) and the change in time (?t) consumed.

Findings

• In the light of the above discussion, we can say that the speed with the direction forms a velocity.
• In order to provide a much better understanding of speed and velocity and their basic differences are listed in the table shown below.

Parameters	Speed	Velocity
Definition	The rate at which a body covers a particular distance is commonly known as speed.	The rate at which a body changes its position in a specific direction is called velocity.
Magnitude	Speed is always positive and it cannot be either negative or zero.	Velocity can be positive, zero, and negative depending upon the direction in which an object is moving.
Quantity Type	Speed does not need any direction for its description so, it is a scalar quantity.	Velocity cannot be described without direction so it is a vector quantity.
Change in Direction	Change in direction does not matter when calculating average speed.	Every change in direction changes the velocity.
Formula	s=distancetime=dt	s=change in positionchange in time=st
SI Units	Meter per second (m/s)	Meter per second (m/s)

Examples of Velocity

A few examples of velocity from real-life are presented to clear your concepts related to it if there still exists any confusion.

• Suppose, you go to your school to maintain your studies on a daily basis. The school is situated to the west of your home. Here, you can observe that you always go towards the west from the starting point which means you go in a particular direction that depicts velocity. Your speed could be high or low.
• In the game of cricket, when a ball is thrown by the baller towards a batsman is also a great example of velocity from our daily life because it follows a single direction.
• The way the moon revolves around the earth and the earth moves around the sun is another example of velocity from nature because of its single direction.
• The ceiling fan rotating in your home during summers also belongs to the family of velocity due to its either clockwise or anti-clockwise rotation.
• The movement of the train from one city to another also follows a specific track in a single direction.
• A revolution of a launched satellite around the earth.
• Water coming from the tap when you open it.
• The flow of the river (it depicts variable velocity).
• Anyone doing morning walk or running.

Final Words

This is all from today’s article. I have tried my level best to explain to you each and everything associated with the velocity. I have focused in detail on its basic concept, various forms, unit assigned by System International, and visual examples where needed. Moreover, I have provided you with a couple of examples captured from real life so that you can have a better understanding of velocity.

I hope you have enjoyed the content and are well aware of this topic now. If you are looking for more similar information, stay tuned because I have a lot more to share with you guys in the upcoming days. In case you have any concerns, you can ask me in the comments. I will surely try to help you out as much as I can. For now, I am signing off. Take good care of yourself and stay blessed always.

Thank You!

What is Physics? Definition, Branches, Books and Scientists

Hello Friends! I hope you all are doing well. Today, I am going to give you a very basic and detailed tutorial on What is Physics? We will also discuss Physics branches, popular Physics books, famous physicians, great inventions in the field of Physics etc. When I was thinking of writing this tutorial on Physics, the first thing came to my mind was "Big Bang Theory" (the TV show, not the event itself). Sheldon was a Physicist & in season finale, he won Nobel Prize in Physics for super asymmetry. In the 19th century, scientists have divided Physical Sciences in 5 major sections:

• Physics.
• Chemistry.
• Metorology.
• Astronomy.
• Geology.

Physics is considered as the most important branch of Science & mainly focuses on energy & matter. Let's discuss in detail: What is Physics?

What is Physics?

Fundamentaly, this universe is divided into 3 main categories, named as:

• Extremely-Large matter: It involves planets, galaxies etc.
• Extremely-Small matter: It involves micro-structures i.e. electrons, neutrons, protons etc.
• Middle-Sized matter: It involves wide range of matter ranging from small objects to Earth itself.

Physics is all about this middle-sized matter & their energies. In physics, we analyse all naturally occuring processes/laws and their effects on matter i.e. motion laws, space & time quantum, forces holding objects together, transmission of energy, physical properties, compositions of different matter etc. So, now let's have a look at a proper Physics Definition:

Physics Definition

• Physics(originated from Latin word Physica means ‘natural thing’) is a field of science, mainly focuses on matter & energy and the relationship between them.
• It provides the mathematical formulas for all natural activities happening on our planet earth.
• Physcics involves the study of all natural laws defined for matters or forces i.e. heat, light, magnetism, sound, nuclear etc.
• Physics is considered as the most fundamental branch of science and is divided into numerous sub-branches.
• Physics has also provided many fundamental laws which formulated the basis of other science branches.

Physics Overlapping

• Physics has also overlapped with other fundamental branches of science & formulated new advanced branches, few of them are:
  • BioPhysics.
  • AstroPhysics.
  • Physical Chemistry.
  • Health Physics.

Now, let's answer this question: Why is Physics important?

Why is Physics important?

Plysics plays an important role in improving our everyday life. If we look around, we will find application of Physics in almost every thing. Our transport system is the foremost application of Physics as it involves inertial laws, thermodynamics knowledge, vehicle's structure etc. We have seen a rapid growth in science which has become possible mainly because of Physics. Let's have a look at few important daily life fields using Physics Laws:

• Transportantion vehicles.
• Irrigation systems.
• Home appliances.
• Communication systems.
• Measuing Instruments.
• Medical Equipments.
• Weather Forcasting.
• Defensive Systems.
• Nuclear Energy.
• Space Travel.

Branches of Physics

As we have discussed, physics deals with middle-sized matter so its applications range from a simple tyre to nuclear energy and thus it is further divided into several branches. Few of Physics branches are as follows:

1. Mechanics

• It deals with motion of objects, why & how is motion produced in different objects and what are the effects of different types of motions.

2. Thermodynamics

• It deals with heat energy, how is heat transffered from one object to another and effects generated by heat.

3. Sound

• It studies the physcial behavior of sound energy, how is it produced, travelled and transformed.

4. Light (Optics)

• It studies the physical behavior of Light energy, how is it produced, travelled and transformed.

5. Electricity & Magnetism

• It studies the physical behavior of electrical charges i.e. either moving or at rest, alongwith its relationship with magnetism.

6. Atomic Physics

• It deals with the study of physical structure & activities of atoms.

7. Nuclear Physics

• It deals with the study of nuclei & the energy it releases under different circumstances.

8. GeoPhysics

• It studies the structure, behavior, forces etc. related to Earth.

9. Biophysics

• It is the deep experimental study of biological problems using laws of physics.
• One of the outstanding and remarkable discoveries happened under this branch is the DNA structure by James Watson.

10. Astrophysics

• It deals with the study of universe i.e. planet, galaxies, and stars using laws of physics.

Other Physics Branches

Few other physics branches are as follows:

1. Cosmology
2. Plasma Physics
3. Condensed Matter
4. General physics
5. Optics & Lasers
6. Mathematical Physics
7. Nonlinear Dynamics.
8. Quantum Mechanics
9. Mathematical Methods
10. Statistical Mechanics and Entropy
11. Numerical Methods or Simulations
12. Classical Mechanics
13. Nuclear Physics
14. Atomic Physics
15. Astronomy
16. Special Relativity
17. Fluid Dynamics
18. General Relativity

Popular Books of Physics

Although numerous books have been publised, discussed difference aspects of Physics or Physicists. Here I have mentioned two of my favorite Physics books:

1. What is Real?

• What is Real? This Physics book tells the gripping stories about the ideology and the courage of physicists, who stand up for the truth.

2. For the Love of physics

• This book provides the wide range of information about different energies and its forms.

Few other Physics Books

Some other famous physics books are listed below:

1. You have changed my life.
2. The Feynman Lectures on Physics.
3. Physics of the Impossible.
4. Seven Brief Lessons on Physics.
5. The Physics of Time.
6. Relativity: The Special and the General Theory.
7. Astrophysics for People in a Hurry.
8. The Universe in a Nutshell.
9. The Strange Theory of Light and Matter.
10. A Brief History of Time.

Greatest Physics Scientists(Physicists) of all Times

Physics has evolved with time. There's a long list of real world heroes, who have made Physics their passion and because of their fruitful efforts, today we have lucuries in our lives. Let's have a look at few of world's greatest physicists:

Greatest Physics Scientists(Physicists) of all Times
No.	Physicist Name	Achievement
1	Albert Einstein	Theory of Relativity(E=mc2), Quantum light theory, Avogadro's Number etc.
2	Isaac Newton	Laws of motion, Gravitational force etc.
3	Nikola Tesla	Worked mostly in Electrical Energy.
4	William Gilbert	Proposed that Earth is a giant magnet.
5	Willbrod Snell	Laws of refraction i.e. Snell's Laws.
6	Galileo Galilei	worked in astrophysics.
7	Blaise Pascal	Famous for Pascal's Laws.
8	Daniel Bernoulli	Famous for Bernoulli's Theorem. (Fluid Flow)
9	Christiaan	Famous for Hagen’s Principle. (Geometrical Theory for Light)
10	Benjamin Franklin	He discovered electrical charges.
11	Leonard Euler	Worked in Fluid dynamics, Lunar Theory, Mechanics etc.
12	Henry Cavendish	Worked in GeoPhysics.
12	Joseph Louis	Worked in Mechanics.
12	Robert Milikan	Worked on charges & cosmic rays etc.
12	C. Wilson	worked in GeoPhysics.

Few remarkable Physicists

Here's the list of few other remarkable physicists:

• Sir O. Richardson
• L. Ernest Rutherford
• Guglielmo Marconi
• Johannes Stark
• S. Chandrasekhara Raman
• C. Glover Barkla
• Albert Einstein
• Otto Hahn
• Max von Laue
• P. A. Carruthers
• James Franck
• V. Franz Hess
• Peter Debye
• Niels Bohr
• D. J. Thouless
• Gustav Hertz
• Erwin Schrödinger
• Otto Stern
• K. M. Georg Siegbahn
• P. Williams Bridgman
• J. Baptiste Perrin
• G. A. Baym
• Stanley J. Brodsky
• Haim Harari
• K. S. Thorne
• Francesco Iachello
• Gabriele Veneziano
• Chris Quigg
• Howard Georgi
• J. Dirk Walecka
• Nathan Isgur
• Edward Witten
• R. Charles Merkle
• O. Wallace Greenberg
• K. Eric Drexler
• Nathan Seiberg
• Stephen Wolfram
• John N. Bahcall
• Stanley Mandelstam
• Peter Higgs
• A. Arima
• Joel Lebowitz
• J. P. Schiffer
• T. A. Witten
• Kenneth Fowler
• Tullio Regge
• M. S. Dresselhaus
• Daniel Kleppner
• Jeffrey Goldstone
• Ludvig Faddeev
• J.D. Bjorken

I hope this article will help to understand the basics of physics & its importance in our everyday life. If you have any questions/suggestions, please use the comments section below. Thanks for reading. Have a good day. :)