Compilation of Physics Equations

For the sake of myself and other students taking Physics (and who happen to luckily chance upon this blog), I shall compile all of the formulas inside my Physics textbook for easier reference as well as memorizing. You can always thank me after you score an A1 for your Physics. XD

Average speed

v = d ÷ t,

where v = average speed,
d = total distance moved,
t = total time taken

Average velocity

v = d ÷ t,

where v = average velocity,
d = total displacement (linear distance),
t = total time taken

Acceleration

a = v ÷ t

where a = acceleration,
v = change in velocity,
t = time taken

Force

F = ma,

where F = resultant force (in Newton (N)),
m = mass of object (in kilograms (kg)),
a = acceleration of object (in metres per second square (m s^-2))

Weight

W = mg,

where W = weight of object (in Newton (N)),
m = mass of object (in kilograms (kg)),
g = gravitational field strength (in metres per second square (m s^-2) or Newton per kilogram (N kg^-1))

Density

ρ = m ÷ V,

where ρ = density of substance,
m = mass of substance,
V = volume of substance

Moment of a force

τ = F x d,

where τ = moment of a force (in Newton metre (N m)),
F = force (in Newton (N)),
d = perpendicular distance from line of action of the force to the pivot (in metre (m))

Work done

W = F x d,

where W = work done by a constant force (in joules (J)),
F = constant force (in Newton (N)),
d = distance moved in the direction of the force (in metre (m))

Kinetic energy

E_k = ½mv²,

where E_k = kinetic energy (in joules (J)),
m = mass of body (in kilograms (kg)),
v = speed of body (in metre per second (m s-1))

Gravitational potential energy

E_p = mgh,

where E_p = gravitational potential energy (in joules (J)),
m = mass of body (in kilograms (kg)),
g = gravitational field strength (in metres per second square (m s^-2) or Newton per kilogram (N kg^-1)),
h = height to which the object is raised (in metres (m))

Efficiency

Efficiency = useful energy output ÷ energy input x 100%

Efficiency is calculated in percentage
Energy is calculated in joules (J)

Power

P = W ÷ t = E ÷ t,

where P = power (in watt (W)),
W = work done (in joules (J)),
E = energy converted (in joules (J)),
t = time taken (in seconds (s))

Pressure

p = F ÷ A,

where p = pressure (in Newton per square metre (N m^-2) or Pascal (Pa)),
F = force (in Newton (N)),
A = area where force is action on (in square metre (m²))

Pressure in liquids

p = hρg,

where p = pressure in liquid due to liquid column (in Newton per square metre (N m^-2) or Pascal (Pa)),
h = height of column or depth of liquid (in metres (m)),
ρ = density of liquid (in kilogram per cubic metre (kg m^-3),
g = gravitational field strength (in metres per second square (m s^-2) or Newton per kilogram (N kg^-1))

Transmission of Pressure in Liquids

P_Y = P_X
F_Y ÷ A_Y = F_X ÷ A_X,

where P_Y = Pressure at Y (in Newton per square metre (N m^-2) or Pascal (Pa)),
P_X = Pressure at X (in Newton per square metre (N m^-2) or Pascal (Pa)),
F_Y = Force acting downwards at Y (in Newton (N)),
F_X = Force acting downwards at X (in Newton (N)),
A_Y = Area of Piston Y (in square metre (m²)),
A_X = Area of Piston X (in square metre (m²))

Pressure-volume relationship of a gas

p₁V₁ = p₂V₂,

where p₁ = initial pressure (in Newton per square metre (N m^-2) or Pascal (Pa)),
p₂ = final pressure (in Newton per square metre (N m^-2) or Pascal (Pa)),
V₁ = initial volume (in cubic metre (m³) or cubic centimetre (cm³)),
V₂ = final volume (in cubic metre (m³) or cubic centimetre (cm³))

((Why not we have Initial Release (Shikai) and Final Release (Bankai) instead?? XD))

Converting mm Hg to Pascal

P = p_B × ρ × g,

where P = Pressure (in pascal (Pa)),
p_B = Pressure (in m Hg (1mm Hg = 10^-3 m Hg)),
ρ = density of mercury (in kg m^-3) = 13.6 x 10₃ kg m-3,
g = gravitational strength (in m s^-2)

Calculating temperature on the Centigrade scale

θ = (l_θ - l₀) ÷ (l₁₀₀ - l₀) x 100,

where θ = temperature of unknown body (in degrees Celsius (°C)),
l_θ = length of liquid level when bulb is immersed in unknown body whose temperature is to be determined (in centimetres (cm)),
l₀ = length of liquid level when bulb is immersed in pure melting ice (in centimetres (cm)),
l₁₀₀ = length of liquid level when bulb is immersed in steam (in centimetres (cm))

Kelvin scale

θ = T - 273,

where θ = temperature (in degrees Celsius (°C)),
T = temperature (in Kelvin (K))

Heat Capacity

C = Q ÷ Δθ,

where C = heat capacity (in joules per Kelvin (J K^-1) or joules per degrees Celsius (J °C^-1)),
Q = heat absorbed (in joules (J)),
Δθ = change in temperature (in Kelvin (K) or degrees Celsius (°C))

Specific Heat Capacity

Q = mcΔθ,

where Q = heat absorbed (in joules (J)),
m = mass of substance (in kilograms (kg)),
c = specific heat capacity (in joules per kilogram per Kelvin (J kg^-1 K^-1) or joules per kilogram per degrees Celsius (J kg^-1 °C^-1)),
Δθ = change in temperature (in Kelvin (K) or degrees Celsius (°C))

Latent Heat of Fusion

L_f = l_f x m,

where L_f = latent heat of fusion (in joules (J)),
l_f = specific latent heat of fusion (in joules per kilogram (J kg-1)),
m = mass of solid (in kilograms (kg))

Latent Heat of Vaporisation

L_v = l_v x m,

where L_v = latent heat of vaporisation (in joules (J)),
l_v = specific latent heat of vaporisation (in joules per kilogram (J kg-1)),
m = mass of liquid (in kilograms (kg))

Properties of Wave Motion

T = 1 ÷ f,

where T = period, or the time taken to produce one complete wave (in seconds (s)),
f = frequency, or the number of complete waves produced per second (in Hertz (Hz))

v = fλ,

where v = wave speed, or distance travelled by a wave in one second (in metres per second (m s^-1)),
f = frequency, or the number of complete waves produced per second (in Hertz (Hz)),
λ = wavelength, or the shortest distance between any two points on a wave that are in a phase (in metres (m))

Refraction

n = sin i ÷ sin r = c ÷ v,

where n = refractive index of a medium,
i = angle of incidence (angle between incident ray and normal, in degrees (°)),
r = angle of refraction (angle between refracted ray and normal, in degrees (°)),
c = speed of light in vacuum (in metre per second (m s^-1)),
v = speed of light in medium (in metres per second (m s^-1))

Linear magnification of Converging lens

m = h₁ ÷ h₀ = v ÷ u,

where m = linear magnification,
h₁ = height of image (in metres (m) or centimetres (cm)),
h₀ = height of object (in metres (m) or centimetres (cm)),
v = distance of image (in metres (m) or centimetres (cm)),
u = distance of object (in metres (m) or centimetres (cm)),

Static Charge and Electric Current

I = Q ÷ t,

where I = current (in coulomb (C)),
Q = charge (in ampere (A)),
t = time (in seconds (s))

Electromotive Force (E.M.F) and Potential Difference (P.D.)

E = W ÷ Q,

where E = e.m.f. (in volts (V)),
W = energy converted from non-electrical forms to electrical forms (in joules (J)),
Q = positive charge (in coulomb (C))

V = W ÷ Q,

where V = potential difference (in volts (V)),
W = energy converted from electrical forms to non-electrical forms (in joules (J)),
Q = charge (in coulomb (C))

Resistance

R = V ÷ I,

where R = resistance of a material (in ohm (Ω)),
V = potential difference across the material (in volts (V)),
I = current flowing in the material (in ampere (A))

R = ρl ÷ A,

where R = resistance of a material (in ohm (Ω)),
ρ = resistivity of the material (in ohm metre (Ω m)),
l = length of wire (in metres (m)),
A = cross-sectional area of wire (in square metres (m²))

Electric Circuits – Series

R = R₁ + R₂ + R₃ + ... + R_n,

where R = combined resistance in the circuit (in ohm (Ω)),
R₁ = resistance of the first resistor in the circuit (in ohm (Ω)),
R₂ = resistance of the second resistor in the circuit (in ohm (Ω)),
R₃ = resistance of the third resistor in the circuit (in ohm (Ω)),
R_n = resistance of the last resistor in the circuit (in ohm (Ω))

I = I₁ = I₂ = I₃ = ... = I_n,

where I = current flowing in the circuit (in coulomb (C)),
I₁ = current flowing in the first resistor in the circuit (in coulomb (C)),
I₂ = current flowing in the second resistor in the circuit (in coulomb (C)),
I₃ = current flowing in the third resistor in the circuit (in coulomb (C)),
I_n = current flowing in the last resistor in the circuit (in coulomb (C))

V = V₁ + V₂ + V₃ + ... + V_n,

where V = potential difference across the whole circuit (in volts (V)),
V₁ = potential difference across the first resistor (in volts (V)),
V₂ = potential difference across the second resistor (in volts (V)),
V₃ = potential difference across the third resistor (in volts (V)),
V_n = potential difference across the last resistor (in volts (V))

Electric Circuits – Parallel

1 ÷ R = 1 ÷ R₁ + 1 ÷ R₂ + 1 ÷ R₃ + ... + 1 ÷ R_n,

where R = combined resistance in the circuit (in ohm (Ω)),
R₁ = resistance of the first resistor in the circuit (in ohm (Ω)),
R₂ = resistance of the second resistor in the circuit (in ohm (Ω)),
R₃ = resistance of the third resistor in the circuit (in ohm (Ω)),
R_n = resistance of the last resistor in the circuit (in ohm (Ω))

I = I₁ + I₂ + I₃ + ... + I_n,

where I = current flowing in the circuit (in coulomb (C)),
I₁ = current flowing in the first resistor in the circuit (in coulomb (C)),
I₂ = current flowing in the second resistor in the circuit (in coulomb (C)),
I₃ = current flowing in the third resistor in the circuit (in coulomb (C)),
I_n = current flowing in the last resistor in the circuit (in coulomb (C))

V = V₁ = V₂ = V₃ = ... = V_n,

where V = potential difference across the whole circuit (in volts (V)),
V₁ = potential difference across the first resistor (in volts (V)),
V₂ = potential difference across the second resistor (in volts (V)),
V₃ = potential difference across the third resistor (in volts (V)),
V_n = potential difference across the last resistor (in volts (V))

Measurement of Electrical Power and Energy

P = IV,

where P = power of electrical appliance (in watts (W)),
I = current flowing through it (in ampere (A)),
V = potential difference across it (in volts (V))

E = Pt,

where E = electrical energy (in joules (J)),
P = power (in watts (W)),
t = time (in seconds (s))

Transformers (I shall whack whoever says "robots in disguise")

V_s ÷ V_p = N_s ÷ N_p = I_p ÷ I_s,

where V_s = secondary output voltage (in volts (V)),
V_p = primary input voltage (in volts (V)),
N_s = number of turns in secondary coil,
N_p = number of turns in primary coil,
I_p = current in primary coil (in ampere (A)),
I_s = current in secondary point (in ampere (A))

Take extra note of the current. It is current in primary coil divided by current in secondary coil, not the other way round, like voltage and number of turns!

And yes, Yoshida, you can calculate the current in a transformers question, so don’t go and write "Not applicable" again. -_-

P_loss = (P_out)² ÷ V² x R,

where Ploss = power lost as heat during transmission of electrical power (in watts (W)),
Pout = electrical power output (in watts (W)),
V = potential difference (in volts (V)),
R = resistance of supply lines (in ohm (Ω))

And for the fucking sake of completion, the last and final equation, even though it is out of the god damned syllabus:

Nuclear Energy

E = mc²,

where E = energy (in joules (J)),
m = mass (in kilograms (kg)),
c = velocity of light (in metres per second (m s^-1))