This cheat sheet covers important formulae and conversions of chapter physics - units and dimensions
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The physical quantities that depend on other quantities and can be derived from other physical quantities are known as derived quantities.
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The units of derived physical quantities are called as derived units.
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Example : Area, Volume, Density etc.
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Fundamental Quantity
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Unit
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Symbol
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Length
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Meter
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m
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Mass
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Kilogram
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Kg
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Time
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Second
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s
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Electric current
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Ampere
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A
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Temperature
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Kelvin
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k
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Intensity of light
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Candela
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cd
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Quantity of substance
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Mole
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mol
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Supplementery Quantities
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Plane angle
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Radian
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rad
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Solid Angle
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Steradian
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sr
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Physical Quantity
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Formula
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Dimensional Formula
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Area (A)
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Length x Breadth
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[M0L2T0]
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Speed (s)
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Distance / Time
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[M0L1T-1]
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Velocity (v)
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Displacement / Time
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[M0L1T-1]
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Acceleration (a)
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Change in velocity / Time
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[M0L1T-2]
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Linear momentum (p)
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Mass x Velocity
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[M1L1T-1]
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Force (F)
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Mass x Acceleration
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[M1L1T-2]
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Work (W)
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Force x Distance
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[M1L2T-2]
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Energy (E)
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Work
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[M1L2T-2]
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Impulse (I)
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Force x Time
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[M1L1T-1]
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Pressure (P)
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Force / Area
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[M1L-1T-2]
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Power (P)
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Work / Time
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[M1L2T-3]
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Angular velocity( ω )
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Angle / Time
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[M0L0T-1]
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Angular acceleration( α )
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Angular velocity / Time
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[M0L0T-2]
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Angular momentum (J)
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Moment of inertia x Angular velocity
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[M1L2T-1]
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Torque (𝞽)
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Moment of inertia x Angular acceleration
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[M1L2T-2]
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Temperature
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——
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[M0L0T0K1]
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Heat (Q)
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Energy
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[M1L2T-2]
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Latent heat (L)
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Heat / Mass
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[M0L2T-2]
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The physical quantities that do not depend on other quantities and exits independently are known as fundamental or base quantities.
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The units of fundamental quantities are called as fundamental units.
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Example : Length, Mass, Time etc.
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Measurement of any physical quantity is expressed in terms of an internationally accepted certain basic standard called unit.
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Four main system of representation of units are,
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FPS - Foot pound second
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CGS - Centimeter gram second
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MKS - Meter kilogram second
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SI - Internationally system of units.
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Coherent system of units i.e., units are derived by the multiplication or division of set of fundamental units.
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Rational system of units i.e., uses ine unit for one physical quanity.
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S.I is a decimal system and makes the calculation work easy.
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S.I system is a combination of practical and theoretical work.
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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.
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Dimensional Formula
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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.
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Dimensional formula of any quantity can be expressed as [MaLbTcθd]
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where,
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M - Mass
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L - Length
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T - Time
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θ - Temperature
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Dimensional Constant
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The constants having dimensional formulae are called dimensional constants
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Ex : Plank's Constant, universal gravitational constant
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The physical quantity on the left side of the equations should have the same dimensions as on the right side of the equation
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Application of Dimensional Formula
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(a) To verify the correctness of the equation.
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(b) To convert the one system of units to another system.
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(c) To derive relationship among different physical quantities.
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Limitations of Dimensional Method
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(a) The values of dimensionless constants and proportionality constants cannot be determined using dimensional analysis.
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(b) This method is not applicable if an equation is sum or difference of two or more quantities.
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(c) It is not applicable to the trigonometry, logarithmic and exponential functions.
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(d) It cannot be used to find proportionality constants.
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