Density is mass per unit volume Density = mass / volume 
velocity = displacement / time 
Force = rate of change of momentum 
Momentum = mass . velocity 
Power is rate of work done Power = work / time Unit of power is watt
Potential energy (P) PE = m.g.h m = mass g = acceleration due to gravity (9.81m/s^{2}) h = height 
Kinetic energy (P) P = (1/2).m.v^{2} m = mass v = velocity 
Gravity (Force due to gravity) F_{g} : Force of attraction G : Gravitational constant M_{1} : Mass of first object M_{2} : Mass of second object
F_{g} = 
G M_{1} M_{2}

r^{2}


Acceleration due to gravity at a depth ‘d’ from earth surface is :

Acceleration due to gravity at height ‘h’ from earth surface is : h is very much smaller than R

Escape velocity Escape velocity from a body of mass M and radius r is For example if you want to calculate the escape verlocity of sa object from earth then, M is dmass of earth r is radius of earth 
OPTICS Index of refraction n = c/v
n – index of refraction c – velocity of light in a vacuum v – velocity of light in the given material 
Under constant acceleration linear motion v = final velocity u = intitial velocity a = acceleration t = time taken to reach velocity v from u s = displacement
v = u + a t
s = ut + (1/2)a t ^{2}
s = vt – (1/2)a t ^{2}
v^{2} = u^{2} + 2 a s 
Friction force (kinetic friction) When the object is moving then Friction is defined as : F_{f} = μ F_{n} where F_{f} = Friction force, μ= cofficient of friction F_{n} = Normal force 
Linear Momentum Momentum = mass x velocity 
Capillary action The height to which the liquid can be lifted is given by:
γ: liquidair surface tension(T)(T=energy/area) θ: contact angle ρ: density of liquid g: acceleration due to gravity r: is radius of tube

Simple harmonic motion Simple harmonic motion is defined by: d^{2}x/dt^{2} = – k x 
Time period of pendulum

Waves
v = f . λ where ω = Angular frequency, T=Time period, v = Speed of wave, λ=wavelength

Doppler effect Relationship between observed frequency f and emitted frequency f_{0}:
where, v=velocity of wave v_{s}=velocity of source. It is positive if source of wave is moving away from observer. It is negative if source of wave is moving towards observer. 
Resonance of a string
where, L: length of the string n = 1, 2, 3… 
Resonance of a open tube of air(approximate)
Approximate frequency = f = 
nv 
2L 
where, L: length of the cylinder n = 1, 2, 3… v = speed of sound 
Resonance of a open tube of air(accurate)
frequency = f = 
nv 
2(L+0.8D) 
where, L: length of the cylinder n: 1, 2, 3… v: speed of sound d:diameter of the resonance tube 
Resonance of a closed tube of air(approximate)
Approximate frequency = f = 
nv 
4L 
where, L: length of the cylinder n = 1, 2, 3… v = speed of sound 
Resonance of a closed tube of air(accurate)
frequency = f = 
nv 
4(L+0.8D) 
where, L: length of the cylinder n: 1, 2, 3… v: speed of sound d:diameter of the resonance tube 
intensity of sound
intensity of sound = 
Sound Power 
area 
intensity of sound in decibel= 10log_{10} 
I 
I_{0}

where I=intensity of interest in Wm^{2} I_{0}=intensity of interest in 10^{12}Wm^{2}

Bragg’s law nλ = 2d sinθ where n = integer (based upon order) λ = wavelength d = distance between the planes θ = angle between the surface and the ray 
de Broglie equation
where p = momentum λ = wavelength h = Planck’s constant v = velocity 
Relation between energy and frequency E = hν where E = Energy h = Planck’s constant ν = frequency 
Davisson and Germer experiment
λ = 
h 


where e = charge of electron m = mass of electron V = potential difference between the plates thru which the electron pass λ = wavelength

Centripetal Force (F)
F = 
m v^{2}

= m ω^{2} r 
r 

Circular motion formula v = ω r
Centripetal acceleration (a) = 
v^{2}

r 

Torque (it measures how the force acting on the object can rotate the object) Torque is cross product of radius and Force Torque = (Force) X (Moment arm) X sin θ T = F L sin θ whete θ = angle between force and moment arm 
Forces of gravitation F = G (m_{1}.m_{2})/r^{2} where G is constant. G = 6.67E – 11 N m^{2} / kg^{2} 
StefanBoltzmann Law The energy radiated by a blackbody radiator per second = P P = AσT^{4} where, σ = StefanBoltzmann constant σ = 5.6703 × 10^{8} watt/m^{2}K^{4} 
Efficiency of Carnot cycle

Ideal gas law P V = n R T P = Pressure (Pa i.e. Pascal) V = Volume (m^{3}) n = number of of gas (in moles) R = gas constant ( 8.314472 .m^{3}.Pa.K^{1}mol^{1}] ) T = Temperatue ( in Kelvin [K])

Boyles law (for ideal gas) P_{1} V_{1} = P_{2}V_{2} T (temperature is constant) 
Charles law (for ideal gas)
V_{1}

= 
V_{2}

T_{1}

T_{2}

P (pressure is constant) 
Translational kinetic energy K per gas molecule (average molecular kinetic energy:)
k = 1.38066 x 10^{23} J/K Boltzmanns constant 
Internal energy of monoatomic gas
n = number of of gas (in moles) R = gas constant ( 8.314472 .m^{3}.Pa.K^{1}mol^{1}] ) 
Root mean square speed of gas
k = 1.38066 x 10^{23} J/K Boltzmanns constant m = mass of gas 
Ratio of specific heat (γ)
C_{p} = specific heat capacity of the gas in a constant pressure process C_{v} = specific heat capacity of the gas in a constant volume process 
Internal entergy of ideal gas Internal entergy of ideal gas (U) = c_{v} nRT

In Adiabatic process no heat is gained or lost by the system. Under adiabetic condition PV^{γ} = Constant TV^{γ1} = Constant where γ is ratio of specific heat.

Boltzmann constant (k)
R = gas constant N_{a} = Avogadro’s number. 
Speed of the sound in gas
R = gas constant(8.314 J/mol K) T = the absolute temperature M = the molecular weight of the gas (kg/mol) γ = adiabatic constant = c_{p}/c_{v} 
Capillary action The height to which the liquid can be lifted is given by h=height of the liquid lifted T=surface tension r=radius of capillary tube

Resistance of a wire
ρ = rsistivity L = length of the wire A = crosssectional area of the wire 
Ohm’s law V = I . R V = voltage applied R = Resistance I = current
Electric power (P) = (voltage applied) x (current) P = V . I = I^{2} . R V = voltage applied R = Resistance I = current 
Resistor combination If resistors are in series then equivalent resistance will be R_{eq} = R_{1} + R_{2} + R_{3} + . . . . . . + R_{n} If resistors are in parallel then equivalent resistance will be 1/R_{eq} = 1/R_{1} + 1/R_{2} + 1/R_{3} + . . . . . . + 1/R_{n} 
In AC circuit average power is : P_{avg} = V_{rms}I_{rms} cosφ where, P_{avg} = Average Power V_{rms} = rms value of voltage I_{rms} = rms value of current 
In AC circuit Instantaneous power is : P_{Instantaneous } = V_{m}I_{m} sinωt sin(ωtφ) where, P_{Instantaneous} = Instantaneous Power V_{m} = Instantaneous voltage I_{m} = Instantaneous current 
Capacitors Q = C.V where Q = charge on the capacitor C = capacitance of the capacitor V = voltage applied to the capacitor 
Total capacitance (Ceq) for PARALLEL Capacitor Combinations: C_{eq} = C_{1} + C_{2} + C_{3} + . . . . . . + C_{n} Total capacitance (Ceq) for SERIES Capacitor Combinations: 1/C_{eq} = 1/C_{1} + 1/C_{2} + 1/C_{3} + . . . . . . + 1/C_{n} 
Parallel Plate Capacitor
where C = [Farad (F)] κ = dielectric constant A = Area of plate d = distance between the plate ε_{0} = permittivity of free space (8.85 X 10^{12} C^{2}/N m^{2}) 
Cylindrical Capacitor
C = 2 π κ ε_{0}

L 
ln (b/a) 
where C = [Farad (F)] κ = dielectric constant L = length of cylinder [m] a = outer radius of conductor [m] b = inner radius of conductor [m] ε_{0} = permittivity of free space (8.85 X 10^{12} C^{2}/N m^{2}) 
Spherical Capacitor
C = 4 π κ ε_{0}

a b 
b – a 
where C = [Farad (F)] κ = dielectric constant a = outer radius of conductor [m] b = inner radius of conductor [m] ε_{0} = permittivity of free space (8.85 X 10^{12} C^{2}/N m^{2}) 
Magnetic force acting on a charge q moving with velocity v F = q v B sin θ where F = force acting on charge q (Newton) q = charge (C) v = velocity (m/sec^{2}) B = magnetic field θ = angle between V (velocity) and B (magnetic field) 
Force on a wire in magnetic field (B) F = B I l sin θ where F = force acting on wire (Newton) I = Current (Ampere) l = length of wire (m) B = magnetic field θ = angle between I (current) and B (magnetic field) 
In an RC circuit (ResistorCapacitor), the time constant (in seconds) is: τ = RC R = Resistance in Ω C = Capacitance in in farads. 
In an RL circuit (Resistorinductor ), the time constant (in seconds) is: τ = L/R R = Resistance in Ω C = Inductance in henries 
Self inductance of a solenoid = L = μn^{2}LA n = number of turns per unit length L = length of the solenoid. 
Mutual inductance of two solenoid two long thin solenoids, one wound on top of the other M = μ_{0}N_{1}N_{2}LA N_{1} = total number of turns per unit length for first solenoid N_{2} = number of turns per unit length for second solenoid A = crosssectional area L = length of the solenoid. 
Energy stored in capacitor

Coulomb’s Law Like charges repel, unlike charges attract. F = k (q_{1} . q_{2})/r^{2} where k is constant. k = 1/(4 π ε_{0}) ≈ 9 x 10^{9} N.m^{2}/C^{2} q_{1} = charge on one body q_{2} = charge on the other body r = distance between them Calculator based upon Coulomb’s Law 
Ohm’s law V = IR where V = voltage I = current R = Resistence

Electric Field around a point charge (q) E = k ( q/r^{2} ) where k is constant. k = 1/(4 π ε_{0}) ≈ 9 x 10^{9} N.m^{2}/C^{2} q = point charge r = distance from point charge (q) 
Electric field due to thin infinite sheet
where E = Electric field (N/C) σ = charge per unit area C/m^{2} ε_{0} = 8.85 X 10^{12} C^{2}/N m^{2} 
Electric field due to thick infinite sheet
where
E = Electric field (N/C) σ = charge per unit area C/m^{2} ε_{0} = 8.85 X 10^{12} C^{2}/N m^{2} 
Magnetic Field around a wire (B) when r is greater than the radius of the wire.
where I = current r = distance from wire and r ≥ Radius of the wire 
Magnetic Field around a wire (B) when r is less than the radius of the wire.
where I = current R = radius of wire r = distance from wire and r ≤ Radius of the wire (R) 
Magnetic Field At the center of an arc
where I = current r = radius from the center of the wire 
Bohr’s model
where L = angular momentum n = principal quantum number = 1,2,3,…n h = Planck’s constant. 
Emitting Photons(Rydberg Formula)
E_{photon} = E_{0}( 
1 
 
1 
) 
n_{1}^{2}

n_{2}^{2}

where n_{1} < n_{2} E_{0} = 13.6 eV 
Half life of radioactive element

Average life of radioactive element
