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
| 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
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:
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
| Simple harmonic motion
Simple harmonic motion is defined by:
d2x/dt2 = - 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 f0:
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
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 |
where
I=intensity of interest in Wm-2
I0=intensity of interest in 10-12Wm-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)
|
Circular motion formula v = ω 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 θ
T = F L sin θ
whete θ = 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 = AσT4
where,
σ = Stefan-Boltzmann constant
σ = 5.6703 × 10-8 watt/m2K4 |
Efficiency of Carnot cycle
| 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)
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 .m3.Pa.K-1mol-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)
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 PVγ = Constant
TVγ-1 = Constant
where γ is ratio of specific heat.
|
Boltzmann constant (k)
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)
γ = 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
| Resistance of a wire
ρ = 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 cosφ
where,
Pavg = Average Power
Vrms = rms value of voltage
Irms = rms value of current | In AC circuit Instantaneous power is :
PInstantaneous = VmIm sinωt sin(ωt-φ)
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
where
C = [Farad (F)]
κ = dielectric constant
A = Area of plate
d = distance between the plate
ε0 = permittivity of free space (8.85 X 10-12 C2/N m2) | Cylindrical Capacitor
where
C = [Farad (F)]
κ = dielectric constant
L = length of cylinder [m]
a = outer radius of conductor [m]
b = inner radius of conductor [m]
ε0 = permittivity of free space (8.85 X 10-12 C2/N m2) |
Spherical Capacitor
where
C = [Farad (F)]
κ = dielectric constant
a = outer radius of conductor [m]
b = inner radius of conductor [m]
ε0 = 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 θ
where
F = force acting on charge q (Newton)
q = charge (C)
v = velocity (m/sec2)
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 (Resistor-Capacitor), the time constant (in seconds) is:
τ = RC
R = Resistance in Ω
C = Capacitance in in farads. |
In an RL circuit (Resistor-inductor ), the time constant (in seconds) is:
τ = L/R
R = Resistance in Ω
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 = μ0N1N2LA
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
|
Coulomb's Law
Like charges repel, unlike charges attract.
F = k (q1 . q2)/r2
where k is constant. k = 1/(4 π ε0) ≈ 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 π ε0) ≈ 9 x 109 N.m2/C2
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/m2
ε0 = 8.85 X 10-12 C2/N m2 |
Electric field due to thick infinite sheet
where
E = Electric field (N/C)
σ = charge per unit area C/m2
ε0 = 8.85 X 10-12 C2/N m2 | 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)
| Ephoton = E0( | 1 | - | 1 | ) |
| n12 | n22 |
where
n1 < n2
E0 = 13.6 eV |
| Half life of radioactive element | Average life of radioactive element |
