IST CHAPTER UNITS & DIMENSION ANALYSICS

UNITS- Question you need ton first understand the meaning of science. Science means MEASUREMENTS. In every field of science we do measurements, science only cares about measuring things. That means the things have to be observable. That’s why in science we don’t take care about FEELINGS. Because we can’t measure feelings. Now as we measure something, we need to represent it in some notation to identify or distinguish between quantities. Because whatever we measure it’s just number, if I say you the speed is 5. What info can you tell about 5, it’s just a number, it nothing tells you about anything related to speed. So you need to specify specific quantities to extract info. Actually speed refers to unit distance travel in unit seconds. So the unit distance can be shown in centimeters, meters, and kilometers. Generally we show distances in meters because it acceptable internationally and it is general notation we use in physics. So the (SI) unit of speed is meters per second. So, you are travelling with 5 meters per second. Meaning that in one second you cover 5 meters distance.

Now units are divided in 3 systems named – 1.MKS SYSTEM 2.CGS SYSTEM 3. FPS SYSTEM

      1. MKS SYSTEM-  M STANDS FOR METERS, K STANDS FOR KILOGRAM, S STANDS FOR SECONDS. IT’S ACCEPTABLE INTERNATIONALLY.

  2. CGS SYSTEM- C- CENTIMETERS, G- GRAMS, S- SECONDS

  3. FPS SYSTEM-  F- FOOT, P- POUND, S- SECONDS,

THESE SYSTEMS EXCEPT IST USED AS SECONDARY UNITS. 

DIMENSION ANALYSIS- IT IS NICE AND AMAZING CONCEPTS. IT IS USED TO CONSTRUCT SOME MATHEMATICAL FORMULAE, AND GREAT RELIEF IN PROBLEM SOLVING EITHER IN COMPETATIVE EXAM OR YOUR HOMEWORK PROBLEM. IN THIS ANALYSIS YOU DON’T HAVE TO WORRY ABOUT DIFFERET SYSTEMS WHICH HAS BEEN USED IN UNITS. IT WORKS SMOOTHLY AND POWERFUL.

IN DIMENSION IT’S ABOUT ONLY LETTER REPERSENTATION. AND WE ENCLOSE DIMENSION WITHIN SQUARE BRACKET [..].

MASS DENOTED BY [M]

DISTANCE OR LENGTH [L]

TIME [T].

CURRENT [A]

CHARGE [C]

€ NOW I AM PRESENTING YOU A QUESTION?  

The dimension of force is [F=MLT ^-2]

Since F = mass times acceleration.

And acceleration has unit meters per second so it has dimension [LT ^-2] hence in this way we can write the dimension of force. And like this you can write down the dimension of any 

Some salient feature about dimension analysis.....

1. All mathematical function such as exponent function or trigonometric function is a dimensionless quantity.

2. If A has some dimension of energy and we express A=B+C or A=B-C

Then B and C having the same dimension as A. Because we can only add or subtract like quantities. This not to be true for multiplication and division. 

3. If A = B/C, then if both B and C having same dimension the quantity A becomes dimensionless i.e. constant. So here if A having dimension of momentum than B and C must be in such a way that they can both become rearrange in terms of momentum. e.g., A = [MLT ^-1] so. And so B should be [ML] and C should be [T ^-1]. This is just only simple example... Or we can say that it’s only simple configuration... Independently A and B may have many kind of such configuration just only for momentum since here we have both B and C is unknown. So in our formula we don't have any constrain what to choose or what not to.