This document contains physics formulae related to mechanics, thermodynamics, electromagnetism, optics, modern physics and more. Some key formulae include: Density = mass / volume, Force = rate of change of momentum, Kinetic energy = (1/2)mv^2, Ohm's law: V=IR, Index of refraction n=c/v, Half life of radioactive element t1/2=ln(2)/λ, Bohr's model: L=nh/2π.

1. PHYSICS FORMULAE
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/s2)
h = height
Kinetic energy (P)
P = (1/2).m.v2
m = mass
v = velocity
Ohm's law
V=I.R

2. V = voltage applied
R = Resistance
I = current
Electric power (P) = (voltage applied) x (current)
P = V . I = I2 . R
V = voltage applied
R = Resistance
I = current
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

3. Density is mass per unit volume velocity = displacement / time
Density = mass / volume
Force = rate of change of momentum Momentum = mass . velocity
Power is rate of work done Kinetic energy (P)
Power = work / time P = (1/2).m.v2
Unit of power is watt m = mass
v = velocity
Potential energy (P)
PE = m.g.h
m = mass
g = acceleration due to gravity (9.81m/s2)
h = height
Gravity (Force due to gravity) Acceleration due to gravity at a depth 'd' from earth
Fg : Force of attraction surface is :
G : Gravitational constant
M1 : Mass of first object d
M2 : Mass of second object gd = g(1- )
R
G M1 M2
Fg =
r2
Acceleration due to gravity at height 'h' from earth Escape velocity
surface is : Escape velocity from a body of mass M and radius r
h is very much smaller than R is
2h
gh = g(1- )
R

4. For example if you want to calculate the escape
velocity of a object from earth then,
M is the mass of earth
r is radius of earth
OPTICS Under constant acceleration linear motion
v = final velocity
Index of refraction u = initial velocity
n = c/v a = acceleration
t = time taken to reach velocity v from u
n - index of refraction s = displacement
c - velocity of light in a vacuum
v - velocity of light in the given material v=u+at
s = ut + (1/2)a t 2
s = vt - (1/2)a t 2
v2 = u2 + 2 a s
Friction force (kinetic friction) Linear Momentum
When the object is moving then Friction is defined as Momentum = mass x velocity
:
Ff = μ Fn
where
Ff = Friction force, μ= coefficient of friction
Fn = Normal force

5. Capillary action Simple harmonic motion
The height to which the liquid can be lifted is given Simple harmonic motion is defined by:
by: d2x/dt2 = - k x
2γcosθ
h=
ρgr
γ: liquid-air surface tension(T)(T=energy/area)
θ: contact angle
ρ: density of liquid
g: acceleration due to gravity
r: is radius of tube
Time period of pendulum Waves
1
f=
T
2π
ω=
T

6. v=f.λ
where
ω = Angular frequency, T=Time period, v = Speed of
wave, λ=wavelength
Doppler effect Relationship between observed Resonance of a string
frequency f and emitted frequency f0:
nv
v frequency = f =
f = f0( ) 2L
v + vs
Where,
Where,
L: length of the string
v=velocity of wave n = 1, 2, 3...
vs=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 open tube of air(approximate) Resonance of a open tube of air(accurate)
nv nv
Approximate frequency = f = frequency = f =
2L 2(L+0.8D)

7. where, where,
L: length of the cylinder L: length of the cylinder
n = 1, 2, 3... n: 1, 2, 3...
v = speed of sound v: speed of sound
d:diameter of the resonance tube
Resonance of a closed tube of air(approximate) Resonance of a closed tube of air(accurate)
nv nv
Approximate frequency = f = frequency = f =
4L 4(L+0.8D)
Where, Where,
L: length of the cylinder
n = 1, 2, 3... L: length of the cylinder
v = speed of sound n: 1, 2, 3...
v: speed of sound
d:diameter of the resonance tube
Intensity of sound Bragg's law
nλ = 2d sinθ
Sound Power
intensity of sound = where
area
n = integer (based upon order)
λ = wavelength
d = distance between the planes
I θ = angle between the surface and the ray
intensity of sound in decibel= 10log10
I0

8. I
dB = 10log10
I0
where
I=intensity of interest in Wm-2
I0=intensity of interest in 10-12Wm-2
de Broglie equation Relation between energy and frequency
h h E = hν
λ= = where
p mv E = Energy
h = Planck's constant
ν = frequency
where
p = momentum
λ = wavelength
h = Planck's constant
v = velocity
Davisson and Germer experiment Centripetal Force (F)
h m v2
λ=
F= = m ω2 r
r
where

9. e = charge of electron
m = mass of electron
V = potential difference between the plates thru which
the electron pass
λ = wavelength
Circular motion formula Torque (it measures how the force acting on the
object can rotate the object)
v=ωr Torque is cross product of radius and Force
Torque = (Force) X (Moment arm) X sin θ
T = F L sin θ
v2 whete θ = angle between force and moment arm
Centripetal acceleration (a) =
r
Forces of gravitation Stefan-Boltzmann Law
The energy radiated by a blackbody radiator per
F = G (m1.m2)/r2 second = P
where G is constant. G = 6.67E - 11 N m2 / kg2 P = AσT4
where,
σ = Stefan-Boltzmann constant
σ = 5.6703 × 10-8 watt/m2K4
Efficiency of Carnot cycle Ideal gas law
PV=nRT
Tc P = Pressure (Pa i.e. Pascal)
η= 1- V = Volume (m3)
Th
n = number of of gas (in moles)

10. R = gas constant ( 8.314472 .m3.Pa.K-1mol-1] )
T = Temperature ( in Kelvin [K])
Boyles law (for ideal gas) Charles law (for ideal gas)
P1 V1 = P2V2
T (temperature is constant) V1 V2
=
T1 T2
P (pressure is constant)
Translational kinetic energy K per gas molecule Internal energy of monatomic gas
(average molecular kinetic energy:)
3
3 K= nRT
K= kT 2
2
n = number of of gas (in moles)
-23
k = 1.38066 x 10 J/K Boltzmann’s constant R = gas constant ( 8.314472 .m3.Pa.K-1mol-1] )

11. Root mean square speed of gas Ratio of specific heat (γ)
3kT Cp
V2rms = γ=
m Cv
k = 1.38066 x 10-23 J/K Boltzmann’s constant Cp = specific heat capacity of the gas in a constant
m = mass of gas pressure process
Cv = specific heat capacity of the gas in a constant
volume process
Internal energy of ideal gas In Adiabatic process no heat is gained or lost by the
system.
Internal energy of ideal gas (U) = cv nRT Under adiabatic condition
PVγ = Constant
TVγ-1 = Constant
where γ is ratio of specific heat.
Cp
γ=
Cv

12. Boltzmann constant (k) Speed of the sound in gas
R
k= R = gas constant(8.314 J/mol K)
Na T = the absolute temperature
M = the molecular weight of the gas (kg/mol)
γ = adiabatic constant = cp/cv
R = gas constant
Na = Avogadro's number.
Capillary action Resistance of a wire
The height to which the liquid can be lifted is given ρL
by R=
A
h=height of the liquid lifted
T=surface tension
r=radius of capillary tube ρ = resistivity
L = length of the wire
2T A = cross-sectional area of the wire
h=
ρrg
Ohm's law Resistor combination
V=I.R If resistors are in series then equivalent
V = voltage applied resistance will be
R = Resistance Req = R1 + R2 + R3 + . . . . . . + Rn
I = current
Electric power (P) = (voltage applied) x (current) If resistors are in parallel then equivalent
P = V . I = I2 . R resistance will be
V = voltage applied 1/Req = 1/R1 + 1/R2 + 1/R3 + . . . . . . + 1/Rn
R = Resistance
I = current

13. In AC circuit average power is : In AC circuit Instantaneous power is :
Pavg = VrmsIrms cosυ PInstantaneous = VmIm sinωt sin(ωt-υ)
where, where,
Pavg = Average Power PInstantaneous = Instantaneous Power
Vrms = rms value of voltage Vm = Instantaneous voltage
Irms = rms value of current Im = Instantaneous current
Capacitors Total capacitance (Ceq) for PARALLEL Capacitor
Q = C.V Combinations:
where Ceq = C1 + C2 + C3 + . . . . . . + Cn
Q = charge on the capacitor Total capacitance (Ceq) for SERIES Capacitor
C = capacitance of the capacitor Combinations:
V = voltage applied to the capacitor 1/Ceq = 1/C1 + 1/C2 + 1/C3 + . . . . . . + 1/Cn
Parallel Plate Capacitor Cylindrical Capacitor
A L
C = κ ε0 C = 2 π κ ε0
d ln (b/a)
where where
C = [Farad (F)] C = [Farad (F)]
κ = dielectric constant κ = dielectric constant
A = Area of plate L = length of cylinder [m]
d = distance between the plate a = outer radius of conductor [m]
ε0 = permittivity of free space (8.85 X 10-12C2/N m2) b = inner radius of conductor [m]
ε0 = permittivity of free space (8.85 X 10-12 C2/N m2)

14. Spherical Capacitor Magnetic force acting on a charge q moving with
velocity v
ab F = q v B sin θ
where
C = 4 π κ ε0
F = force acting on charge q (Newton)
b-a q = charge (C)
where v = velocity (m/sec2)
C = [Farad (F)] B = magnetic field
κ = dielectric constant θ = angle between V (velocity) and B (magnetic field)
a = outer radius of conductor [m]
b = inner radius of conductor [m]
ε0 = permittivity of free space (8.85 X 10-12C2/N m2)
Force on a wire in magnetic field (B) In an RC circuit (Resistor-Capacitor), the time
F = B I l sin θ constant (in seconds) is:
where τ = RC
F = force acting on wire (Newton) R = Resistance in Ω
I = Current (Ampere) C = Capacitance in farads.
l = length of wire (m)
B = magnetic field
θ = angle between I (current) and B (magnetic field)
In an RL circuit (Resistor-inductor ), the time constant Self inductance of a solenoid = L = μn2LA
(in seconds) is: n = number of turns per unit length
τ = L/R L = length of the solenoid.
R = Resistance in Ω
C = Inductance in henries

15. Mutual inductance of two solenoid two long thin Energy stored in capacitor
solenoids, one wound on top of the other
M = μ0N1N2LA 1
N1 = total number of turns per unit length for first
E= CV2
solenoid
N2 = number of turns per unit length for second 2
solenoid
A = cross-sectional area
L = length of the solenoid.
Coulomb's Law Ohm's law
Like charges repel, unlike charges attract.
F = k (q1 . q2)/r2 V = IR
where k is constant. k = 1/(4 π ε0) ≈ 9 x 109N.m2/C2 where
q1 = charge on one body V = voltage
q2 = charge on the other body I = current
r = distance between them R = Résistance
Electric Field around a point charge (q) Electric field due to thin infinite sheet
E = k ( q/r2 ) σ
where k is constant. k = 1/(4 π ε0) ≈ 9 x 109N.m2/C2
E=
q = point charge
r = distance from point charge (q) 2 ε0
where
E = Electric field (N/C)
σ = charge per unit area C/m2
ε0 = 8.85 X 10-12 C2/N m2

16. Electric field due to thick infinite sheet Magnetic Field around a wire (B) when r is greater
than the radius of the wire.
σ
E= μ0 I
ε0 B=
where 2πr
E = Electric field (N/C) where
σ = charge per unit area C/m2 I = current
ε0 = 8.85 X 10-12 C2/N m2 r = distance from wire
and r ≥ Radius of the wire
Magnetic Field around a wire (B) when r is less Magnetic Field At the center of an arc
than the radius of the wire.
μ0 I υ
μ0 I r B=
B= 4πr
2
2πR
where
where I = current
I = current r = radius from the center of the wire
R = radius of wire
r = distance from wire
and r ≤ Radius of the wire (R)

17. Bohr's model Emitting Photons(Rydberg Formula)
1 1
nh
Ephoton = E0( - )
L= n12 n22
2π
where
L = angular momentum where
n = principal quantum number = 1,2,3,...n n1 < n 2
h = Planck's constant. E0 = 13.6 eV
Half life of radioactive element Average life of radioactive element
ln(2) 1
t1/2 = τ=
λ λ