Cheatography

# physics units & dimensions Cheat Sheet by anna_k16

I have a test coming up in a few days and I'm not the best at physics, so I thought I'd make a few pointers

### units

 when measuring any physical quantity we compare it to a standard reference point known as a unit i) fundam­ental units, these are fundam­ental or base quantities which are not derived ii) derived units, these are the units of other physical quantities and can be expressed as a combin­ation of multiple fundam­ental units (together they are know as the system of units)

### intern­ational system of units

 CGS system- the system where centimeter (L), gram (M), seconds (T) FPS system [british system]- the system where foot (L), pound (M), seconds (T) MKS system- the system where meter (L), kilogram (M), seconds (T)

### Intern­ational system of units

 SI units- it's the present system of units which is intern­ati­onally accepted for measur­ement. It has seven base units which then can be combined with each other to form the derived units

### SI units

 quantity name symbol length meter m mass kilogram kg time second s electric ampere A Thermo­dynamic temper­ature kelvin K Amount of substance mole mol Luminous intensity candela cd

### Dimensions of Physical quantities

 the dimensions of a physical quantity are the powers (or the exponents) to which the base quantities are raised to represent that quantity square brackets [ ] are used to indicate the dimensions An equation obtained by equating a physical quantity with its dimens­ional formula is called the dimens­ional equation of the physical quantity. In other words it can be said that dimens­ional equations represent the dimensions of a physical quantity in terms of the base quantity

### examples

 Volume - [V] = [M0 L3 T0] Speed - [v] = [M0 L T-1] Force - [F] = [M L T-2] Mass density - [p] = [M L-3 T0]

### dimens­ional analysis

 Dimens­ional analysis is the practice of checking relations between physical quantities by identi­fying the dimensions of the physical quanti­ties. These dimensions are indepe­ndent of the numerical multiples and constants It helps us deduce certain relations between different physical quantities and checking the deriva­tion, accuracy and dimens­ional consis­tency of the mathem­atical expres­sions

### applic­ations of dimens­ional analysis

 We make use of dimens­ional analysis for three prominent reasons: 1) To check the consis­tency of a dimens­ional equation 2) To derive the relation between physical quantities in physical phenomena 3) To change units from one system to another

 unites and dimension basic pointers dimens­ional analysis (specific) notes for the entire chapter more notes for the chapter questions pdf of questions HOTS questions

### limita­tions of dimens­ional analysis

 Some limita­tions of dimens­ional analysis are: 1) It doesn’t give inform­ation about the dimens­ional constant. 2) The formula containing trigon­ometric function, expone­ntial functions, logari­thmic function, etc. cannot be derived. 3) It gives no inform­ation about whether a physical quantity is a scalar or vector.