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Physics - Units and dimensions Cheat Sheet by

This cheat sheet covers important formulae and conversions of chapter physics - units and dimensions

Physical quantity

Physical Quantity is a quantity that can be measured or can be quanti­fied.
Examples : Mass, Length, Force.
Physical quantity can be classified into,
1. Fundam­ental or base quanti­ties.
2. Derived Quanti­ties.

Derived Quantities

The physical quantities that depend on other quantities and can be derived from other physical quantities are known as derived quanti­ties.
The units of derived physical quantities are called as derived units.
Example : Area, Volume, Density etc.

S.I System of Units

Fundam­ental Quantity
Unit
Symbol
Length
Meter
m
Mass
Kilogram
Kg
Time
Second
s
Electric current
Ampere
A
Temper­ature
Kelvin
k
Intensity of light
Candela
cd
Quantity of substance
Mole
mol
Supple­mentery Quantities
Plane angle
Radian
rad
Solid Angle
Steradian
sr

Dimens­ional Formulas List

Physical Quantity
Formula
Dimens­ional Formula
Area (A)
Length x Breadth
[M0L2T0]
Speed (s)
Distance / Time
[M0L1T-1]
Velocity (v)
Displa­cement / Time
[M0L1T-1]
Accele­ration (a)
Change in velocity / Time
[M0L1T-2]
Linear momentum (p)
Mass x Velocity
[M1L1T-1]
Force (F)
Mass x Accele­ration
[M1L1T-2]
Work (W)
Force x Distance
[M1L2T-2]
Energy (E)
Work
[M1L2T-2]
Impulse (I)
Force x Time
[M1L1T-1]
Pressure (P)
Force / Area
[M1L-1T-2]
Power (P)
Work / Time
[M1L2T-3]
Angular velocity( ω )
Angle / Time
[M0L0T-1]
Angular accele­ration( α )
Angular velocity / Time
[M0L0T-2]
Angular momentum (J)
Moment of inertia x Angular velocity
[M1L2T-1]
Torque (𝞽)
Moment of inertia x Angular accele­ration
[M1L2T-2]
Temper­ature
——
[M0L0T0K1]
Heat (Q)
Energy
[M1L2T-2]
Latent heat (L)
Heat / Mass
[M0L2T-2]
 

Fundam­ental or Base Quantities

The physical quantities that do not depend on other quantities and exits indepe­ndently are known as fundam­ental or base quanti­ties.
The units of fundam­ental quantities are called as fundam­ental units.
Example : Length, Mass, Time etc.

Units

Measur­ement of any physical quantity is expressed in terms of an intern­ati­onally accepted certain basic standard called unit.
Four main system of repres­ent­ation of units are,
FPS - Foot pound second
CGS - Centimeter gram second
MKS - Meter kilogram second
SI - Intern­ati­onally system of units.

Advantages of SI system

Coherent system of units i.e., units are derived by the multip­lic­ation or division of set of fundam­ental units.
Rational system of units i.e., uses ine unit for one physical quanity.
S.I is a decimal system and makes the calcul­ation work easy.
S.I system is a combin­ation of practical and theore­tical work.

Dimensions

The powers to which the fundam­ental units are to be raised to obtain one unit of the quantity are termed as dimensions of a physical quantity.
Dimens­ional Formula
The expression showing the powers to which the fundam­ental units are to be raised to obtain one unit of a derived quantity is termed as dimens­ional formula of that quantity.
Dimens­ional formula of any quantity can be expressed as [MaLbTcθd]
where,
M - Mass
L - Length
T - Time
θ - Temper­ature
Dimens­ional Constant
The constants having dimens­ional formulae are called dimens­ional constants
Ex : Plank's Constant, universal gravit­ational constant

Homoge­neity, Applic­ations and limita­tions of D.F

The physical quantity on the left side of the equations should have the same dimensions as on the right side of the equation
Applic­ation of Dimens­ional Formula
(a) To verify the correc­tness of the equation.
(b) To convert the one system of units to another system.
(c) To derive relati­onship among different physical quanti­ties.
Limita­tions of Dimens­ional Method
(a) The values of dimens­ionless constants and propor­tio­nality constants cannot be determined using dimens­ional analysis.
(b) This method is not applicable if an equation is sum or difference of two or more quanti­ties.
(c) It is not applicable to the trigon­ometry, logari­thmic and expone­ntial functions.
(d) It cannot be used to find propor­tio­nality constants.
                                           
 

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