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
Gravity (Force due to gravity)
Fg
: Force of attraction
G : Gravitational constant
M1
: Mass of first object
M2
: Mass of second object
Fg = G M1 M2
r2
Acceleration due to gravity at a depth 'd' from earth surface is :
gd = g(1- d )
R
Acceleration due to gravity at height 'h' from earth surface is :
h is very much smaller than R
gh = g(1- 2h )
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


v2
= u2 + 2 a s
Friction force (kinetic friction)
When the object is moving then Friction is defined as :
Ff
= µ Fn
where
Ff
= Friction force, µ= cofficient of friction
Fn
= Normal force
Linear Momentum
Momentum = mass x velocity
Capillary action
The height to which the liquid can be lifted is given by:
h = 2?cos?
?gr

?: liquid-air surface tension(T)(T=energy/area)
?: contact angle
?: density of liquid
g: acceleration due to gravity
r: is radius of tube
Simple harmonic motion
Simple harmonic motion is defined by:
d2
x/dt2 = - k x
Time period of pendulum
Waves
f = 1
T


? = 2 p
T

v = f . ?

where
? = Angular frequency, T=Time period, v = Speed of wave, ?=wavelength


Doppler effect Relationship between observed frequency f and emitted frequency f0:
f = f0( v )
v + vs






where,
v=velocity of wave
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 string
frequency = f = nv
2L






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= 10log10 I
I0





dB = 10log10 I
I0






where
I=intensity of interest in Wm-2

I0
=intensity of interest in 10-12Wm-2
Bragg's law
n? = 2d sin?

where
n = integer (based upon order)
? = wavelength
d = distance between the planes
? = angle between the surface and the ray

de Broglie equation
? = h = h
p mv







where
p = momentum
? = wavelength
h = Planck's constant
v = velocity
Relation between energy and frequency
E = h?
where
E = Energy
h = Planck's constant
? = frequency
Davisson and Germer experiment
? = h







where
e = charge of electron
m = mass of electron
V = potential difference between the plates thru which the electron pass
? = wavelength
Centripetal Force (F)
F = m v2 = m ?2 r
r
Circular motion formula

v = ? r

Centripetal acceleration (a) = v2
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 ?
T = F L sin ?
whete ? = angle between force and moment arm
Forces of gravitation
F = G (m1
.m2)/r2
where G is constant. G = 6.67E - 11 N m2
/ kg2
Stefan-Boltzmann Law
The energy radiated by a blackbody radiator per second = P
P = AsT4

where,
s = Stefan-Boltzmann constant
s = 5.6703 × 10-8
watt/m2K4
Efficiency of Carnot cycle
? = 1 - Tc
Th
Ideal gas law
P V = n R T
P = Pressure (Pa i.e. Pascal)
V = Volume (m3
)
n = number of of gas (in moles)
R = gas constant ( 8.314472 .m3
.Pa.K-1mol-1] )
T = Temperatue ( in Kelvin [K])
Boyles law (for ideal gas)
P1
V1 = P2V2
T (temperature is constant)
Charles law (for ideal gas)
V1 = V2
T1 T2

P (pressure is constant)
Translational kinetic energy K per gas molecule (average molecular kinetic energy:)
K = 3 k T
2

k = 1.38066 x 10-23
J/K Boltzmanns constant
Internal energy of monoatomic gas
K = 3 n R T
2

n = number of of gas (in moles)
R = gas constant ( 8.314472 .m3
.Pa.K-1mol-1] )
Root mean square speed of gas
V2rms = 3 k T
m

k = 1.38066 x 10-23
J/K Boltzmanns constant
m = mass of gas
Ratio of specific heat (?)
? = Cp
Cv

Cp
= specific heat capacity of the gas in a constant pressure process
Cv
= specific heat capacity of the gas in a constant volume process
Internal entergy of ideal gas

Internal entergy of ideal gas (U) = cv nRT

In Adiabatic process no heat is gained or lost by the system.
Under adiabetic condition

PV? = Constant
TV?-1
= Constant
where ? is ratio of specific heat.

? = Cp
Cv


Boltzmann constant (k)
k = R
Na

R = gas constant
Na
= 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)
? = adiabatic constant = cp
/cv
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
h= 2T
?rg
Resistance of a wire
R = ?L
A







? = rsistivity
L = length of the wire
A = cross-sectional 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 = I2
. R
V = voltage applied
R = Resistance
I = current
Resistor combination
If resistors are in series then equivalent resistance will be

Req
= R1 + R2 + R3 + . . . . . . + Rn
If resistors are in parallel then equivalent resistance will be

1/Req
= 1/R1 + 1/R2 + 1/R3 + . . . . . . + 1/Rn
In AC circuit average power is :
Pavg
= VrmsIrms cosf
where,
Pavg
= Average Power
Vrms
= rms value of voltage
Irms
= rms value of current
In AC circuit Instantaneous power is :
PInstantaneous
= VmIm sin?t sin(?t-f)
where,
PInstantaneous
= Instantaneous Power
Vm
= Instantaneous voltage
Im
= 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:
Ceq
= C1 + C2 + C3 + . . . . . . + Cn
Total capacitance (Ceq) for SERIES Capacitor Combinations:

1/Ceq
= 1/C1 + 1/C2 + 1/C3 + . . . . . . + 1/Cn
Parallel Plate Capacitor
C = ? e0 A
d
where
C = [Farad (F)]
? = dielectric constant
A = Area of plate
d = distance between the plate
e0
= permittivity of free space (8.85 X 10-12 C2/N m2)
Cylindrical Capacitor
C = 2 p ? e0 L
ln (b/a)
where
C = [Farad (F)]
? = dielectric constant
L = length of cylinder [m]
a = outer radius of conductor [m]
b = inner radius of conductor [m]
e0
= permittivity of free space (8.85 X 10-12 C2/N m2)
Spherical Capacitor
C = 4 p ? e0 a b
b - a
where
C = [Farad (F)]
? = dielectric constant
a = outer radius of conductor [m]
b = inner radius of conductor [m]
e0
= permittivity of free space (8.85 X 10-12 C2/N m2)
Magnetic force acting on a charge q moving with velocity v
F = q v B sin ?
where
F = force acting on charge q (Newton)
q = charge (C)
v = velocity (m/sec2
)
B = magnetic field
? = angle between V (velocity) and B (magnetic field)
Force on a wire in magnetic field (B)
F = B I l sin ?
where
F = force acting on wire (Newton)
I = Current (Ampere)
l = length of wire (m)
B = magnetic field
? = angle between I (current) and B (magnetic field)
In an RC circuit (Resistor-Capacitor), the time constant (in seconds) is:
t = RC
R = Resistance in O
C = Capacitance in in farads.
In an RL circuit (Resistor-inductor ), the time constant (in seconds) is:
t = L/R
R = Resistance in O
C = Inductance in henries
Self inductance of a solenoid = L = µn2LA
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 = µ0
N1N2LA
N1
= total number of turns per unit length for first solenoid
N2
= number of turns per unit length for second solenoid
A = cross-sectional area
L = length of the solenoid.
Energy stored in capacitor
E = 1 C V 2
2
Coulomb's Law
Like charges repel, unlike charges attract.
F = k
(q1 . q2)/r2
where k
is constant. k = 1/(4 p e0) ˜ 9 x 109 N.m2/C2
q1
= charge on one body
q2
= 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/r2 )
where k
is constant. k = 1/(4 p e0) ˜ 9 x 109 N.m2/C2
q = point charge
r = distance from point charge (q)
Electric field due to thin infinite sheet
E = s
2 e0
where
E = Electric field (N/C)
s = charge per unit area C/m2

e0
= 8.85 X 10-12 C2/N m2
Electric field due to thick infinite sheet
E = s
e0
where

E = Electric field (N/C)
s = charge per unit area C/m2

e0
= 8.85 X 10-12 C2/N m2
Magnetic Field around a wire (B) when r is greater than the radius of the wire.
B = µ0 I
2 p r

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.
B = µ0 I r
2 p R2

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
B = µ0 I f
4 p r

where
I = current
r = radius from the center of the wire
Bohr's model
L = nh
2 p

where
L = angular momentum
n = principal quantum number = 1,2,3,...n
h = Planck's constant.
Emitting Photons(Rydberg Formula)
Ephoton = E0( 1 - 1 )
n12 n22







where
n1
< n2
E0
= 13.6 eV
Half life of radioactive element
t1/2 = ln(2)
?
Average life of radioactive element
t = 1
?