Cheatography

# Physics - Units and dimensions Cheat Sheet by rehman225

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.

 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.