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Physics formulas Display all Items       Hide all Items Chemistry formulas
Physics formulas for high school
Physics formulas for grade 11, grade 12 and under graduates.
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 =  2γcosθ
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

Simple harmonic motion
Simple harmonic motion is defined by:
d2x/dt2 = - k x

Time period of pendulum

Waves
f = 1
T

ω = 2 π
T

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:
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
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
λ =  h  =  h
p mv







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 v2 = m ω2 r
r

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
η =  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 (γ)
γ = 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

PVγ = Constant
TVγ-1 = Constant
where γ is ratio of specific heat.
γ = 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)
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
h=  2T
ρrg

Resistance of a wire
R =  ρL
A







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
C = κ ε0   A 
d
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
C = 2 π κ ε0 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]
ε0 = permittivity of free space (8.85 X 10-12 C2/N m2)

Spherical Capacitor
C = 4 π κ ε0 a b
b - a
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
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 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
E = σ
2 ε0
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
E = σ
ε0
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.
B = μ0 I
2 π 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 π 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 φ
4 π r

where
I = current
r = radius from the center of the wire

Bohr's model
L =  nh
2 π

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)
λ

Average life of radioactive element
τ =  1
λ