Physics Formulae
Physics formulae
Mechanics
Speed = distance meter ( second )-1 ms-1
time
velocity = rate of change of displacement with time ( speed in a given direction ) ms-1
acceleration = final velocity - first velocity meter ( second ) -2 ms-2
time
Linear motion with constant acceleration ( moving in a straight line )
v = u + at u = inital velocity t = time
s = ut + ½at2 v = final velocity s = displacement
v2 = u2 + 2as a = acceleration
Note : for acceleration due to gravity ( g ) by free fall
S = ut + ½at2 but u = 0 a = g s
g = 2s/t2 or g = 2 x slope of the line t2
Momentum = mass x velocity ( Kg ms-1 )
Conservation of momentum : In a closed system
Total momentum before impact = Total momentum after impact
m1u1 + m2 u2 = m1 v1 + m2v2
Force = mass x acceleration ( Newton )
force
f = m x a ( N ) slope = f = m
a
Slope of the line = mass of the object acceleration
Circular motion
Angle in radians = length of the arc q = s ( radians )
radius r
Angular velocity = angle in radians w = q ( ms-1 )
time t
Relationship between linear ( v ) and angular velocity (w ) v = r w
| Linear | Angular |
Centripetal acceleration | a = v2/r ( ms-2) | a = r w2 ( ms-2 ) |
Centripetal force | F = m v2/r ( Newton ) | F = m r w2 ( Newton ) |
Gravity
Weight = mass x acceleration due to gravity w = m x g ( Newtons )
Newton`s law of universal gravitation F = G m1 x m2 F = force
d 2 G = universal gravitation constant
m1 and m2 = masses of the bodies
d = distance between m1 and m2
Relationship between G and g g = G m/d2
Periodic time T = 2p = 1 f = frequency w = angular velocity
w f
Periodic time of a satellite T = 4p2R3 / Gm ( T a R3 ) ( T a 1/m )
Density and pressure
Density = mass r = m Kg m -3
volume v
Pressure = Force ( weight ) P = F ( Pascal N m-2 )
area A
Pressure at a depth in a liquid = density x g x depth P = r g h
Boyles Law : For a fixed mass of gas at constant temperature
Pressure a 1
volume pressure
(pascals)
P1V1 = P2V2 ( If given a problem to solve ) 1/volume (m-3)
Simple harmonic motion and the simple pendulum
Hooks law: Applied force a displacement F = - ks
Simple harmonic motion
Acceleration towards a point a displacement from that point
a a - s
a a - w2 s
Periodic time T = 2p = 1
w f
Periodic time of a simple pendulum T = 2
plength−−−−−√plength
T = 2p
L−−√𝑳
acc. −−−−√due to gravity acc. due to gravity
√g√𝒈
g = 4 p2 L
T2 length
Time 2 è g = 4p2 x slope of the line
Work ( energy ) and Power
Work = Force ( weight ) x distance W = F x s ( Joules )
Potential energy = mass x g x height E p = m g h ( Joules )
Kinetic energy = ½ x mass x ( velocity )2 Ek = ½ m v 2 ( Joules )
Power = work P = W ( Watt )
time t
%
efficiency = Power output x 100
Power input
Levers Moment ( Torque ) = Turning force
Moment of a force = force x perpendicular distance from the force to the fulcrum ( N m )
Moment of a couple : Torque = force x distance T = F x d ( N m )
F = force d = the distance between the couple
Heat
To convert Kelvin to ℃
t = T - 273.15 ( t = ℃
and T = Kelvin )
To convert ℃
to Kelvin T = t + 273.15
Heat lost ( or gained ) = mass x specific heat capacity x temperature change
Q = m x c x ∆
θ (unit of heat = Joule )
Heat needed to change state = mass x specific latent heat latent heat = m x l
Specific latent heat of fusion of ice
Heat lost by the water and calorimeter = heat gained by the melting ice + ice water
( m c ∆𝜃)water + ( m c ∆ 𝜃) calorimeter = ( m l ) ice + ( m c ∆𝜃) ice water
Specific latent heat of vapourisation of steam
Heat gained by the water and calorimeter = heat lost condensing steam + steam water
( m c ∆
θ𝜃
) water + ( m c ∆
𝜃 ) calorimeter = ( m l ) steam + ( m c ∆
θ𝜃
) steam water
Light ( Optics )
Mirror and lens formula 1 + 1 = 1 f = focal length
u v f u = object distance
v = image distance
Magnification = Image ( height or distance ) m = v
Object ( height or distance ) u
Power of a lens = 1 P = 1 m -1
Focal length ( meter ) f
Two lenses in contact Power total = P1 + P2
Refractive index ( η) ( no units )
η = sin i i = angle of incidence
sin r r = angle of refraction
η = real depth
apparent depth
η = 1 η = 1
sin of critical angle Sin C
η = Speed in medium 1 η = c1
Speed in medium 2 c2
Wavelength of light n
λ𝝀
= d sin
θ𝜽
n = fringe order (number of the bright spot)
λ = wavelength of light
d = diffraction grating constant
θ𝜃
= angle the fringe makes
Diffraction grating constant : 500 lines per mm
500 x 10 3 per m
Grating constant = 1 = 0.002 x 10 -3 è d = 2 x 10 -6 m
500 x 10 3
Waves sound and light
Velocity of a wave = frequency x wavelength c = f λ
Doppler effect
Observed frequency = actual frequency x speed of sound
Speed of sound +/- speedof the object
f ` = f c ( - when approaching )
c +/- u ( + when going away )
Fundamental frequency of a stretched string
Frequency = 1 Tension f = 1
√T √𝑻
( frequency = Hertz )
2 length mass per unit length 2l
√μ √𝝁
Electricity
Static electricity
Coulombs law Force = 1 Charge 1 x Charge 2 F = 1 Q1 Q 2
4
πε𝜋𝜀
(Distance between charges) 2 4
πε𝜋𝜀
d 2
Unit of force = Newton
Electric field strength E = Force ( Newton ) E = F N C -1
Charge ( Coulomb ) Q
Electric field strength is the force that acts on unit charge substitute in to Coulombs law
E = 1 Q x 1 N C-1 è E = 1 Q N C-1
4
πε𝜋𝜀
d2 4pe d2
Capacitors
Capacitance = Charge ( coulomb ) C =
QV𝑸𝑽
( C V-1 ) = Farad
Voltage ( volts )
Energy stored in a capacitor Energy ( work ) = ½ capacitance x ( voltage )2 E = ½ C V2 (Joule)
Capacitance = permittivity x common area between plates C =
ϵ𝝐
A
distance between plates d
Current electricity
Work = Charge x voltage W = Q x V => V = W ( Definition of the volt )
Q
Charge = Current x voltage Q = I x t => I = Q ( Definition of current )
t
Voltage = Current x Reststance V = I x R => R = V ( Definition of the ohm
ΩΩ
)
I
Power = Voltage x current P = V x I ( unit of power = Watt )
Resistors in series : R total = R1 + R2 + R3
Resistors in parallel : 1 = 1 + 1 + 1
R total R1 R2 R3
Wheatstone Bridge : R1 = R3
R2 R4
Joules Law Work ( heat ) = ( current ) 2 x resistance x time W = I2 R t ( Joules )
Resistivity = Resistance x Area
ρ𝝆
= RA (
Ω𝛀
m ) ( ohm meter )
Length l
Electricity and magnetisim
Magnetic flux = Magnetic flux density x Area
ϕ𝝓
= BA ( Weber )
Magnetic flux density = Magnetic Flux B =
ϕ𝝓
(Tesla )
Area A
Force on a current carrying conductor in a magnetic field
Force = Magnetic flux density x Currrent x length F = B I L ( unit of force = Newton )
Force on a charge ( q ) travelleing in a magnetic field of magnetic flux density B at a velocity v
Force = Magnetic flux density x charge x velocity of the charge F = B q v (Newton )
If charge = one electron F = B e v ( Newton )
Induced electromotive force ( EMF ) ( Voltage ) ( Faradays law )
Induced EMF = Number of turns in the coil x rate of change of flux with time E = - N d
ϕ𝝓
dt
Lenses Law : The induced emf always opposes the force causing it ( - in the above formula )
Transformer Voltage in = Number of turns in the primary
Voltage out Number of turns in the secondary
Root Mean square voltage ( rms ) V rms = V max
√ √
2
Root mean square current ( rms ) I rms = I max
√ √
2