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
