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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 
[M^{0}L^{2}T^{0}] 
Speed (s) 
Distance / Time 
[M^{0}L^{1}T^{1}] 
Velocity (v) 
Displacement / Time 
[M^{0}L^{1}T^{1}] 
Acceleration (a) 
Change in velocity / Time 
[M^{0}L^{1}T^{2}] 
Linear momentum (p) 
Mass x Velocity 
[M^{1}L^{1}T^{1}] 
Force (F) 
Mass x Acceleration 
[M^{1}L^{1}T^{2}] 
Work (W) 
Force x Distance 
[M^{1}L^{2}T^{2}] 
Energy (E) 
Work 
[M^{1}L^{2}T^{2}] 
Impulse (I) 
Force x Time 
[M^{1}L^{1}T^{1}] 
Pressure (P) 
Force / Area 
[M^{1}L^{1}T^{2}] 
Power (P) 
Work / Time 
[M^{1}L^{2}T^{3}] 
Angular velocity( ω ) 
Angle / Time 
[M^{0}L^{0}T^{1}] 
Angular acceleration( α ) 
Angular velocity / Time 
[M^{0}L^{0}T^{2}] 
Angular momentum (J) 
Moment of inertia x Angular velocity 
[M^{1}L^{2}T^{1}] 
Torque (𝞽) 
Moment of inertia x Angular acceleration 
[M^{1}L^{2}T^{2}] 
Temperature 
—— 
[M^{0}L^{0}T^{0}K^{1}] 
Heat (Q) 
Energy 
[M^{1}L^{2}T^{2}] 
Latent heat (L) 
Heat / Mass 
[M^{0}L^{2}T^{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 [M^{a}L^{b}T^{c}θ^{d}] 
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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