Physics Quick Revision

Force

[MLT⁻²]

Energy

[ML²T⁻²]

Pressure

[ML⁻¹T⁻²]

1st eqn

v = u + at

2nd eqn

s = ut + ½at²

3rd eqn

v² = u² + 2as

nth-sec dist

sₙ = u + a(2n−1)/2

Projectile range

R = u² sin2θ / g

Max height

H = u² sin²θ / 2g

Time of flight

T = 2u sinθ / g

Trajectory

y = x tanθ − gx²/(2u²cos²θ)

Centripetal a

v²/r = ω²r

Vertical loop min v (top)

√(gr)

Vertical loop min v (bottom)

√(5gr)

Conical pendulum T

2π√(L cosθ /g)

Work

W = F·d cosθ

KE

½ mv²

PE (gravity)

mgh

Spring PE

½ kx²

Power

P = W/t = F·v

Elastic collision v₁'

((m₁−m₂)u₁ + 2m₂u₂)/(m₁+m₂)

COM

x_cm = Σmᵢxᵢ/Σmᵢ

Torque

τ = r × F = Iα

Ang. momentum

L = Iω = r × p

KE_rot

½ Iω²

Rolling KE

½mv²(1 + I/mr²)

Force

F = GMm/r²

g at height h

g(1 − 2h/R)

g at depth d

g(1 − d/R)

Escape v

√(2gR) = 11.2 km/s Earth

Orbital v

√(gR) at surface; √(GM/r)

Kepler T²

∝ r³

PE

−GMm/r

Linear expansion

ΔL = αLΔT

Heat

Q = mcΔT

Latent heat

Q = mL

Conduction

Q/t = kAΔT/L

Stefan

P = εσAT⁴

Wien

λ_m T = 2.9×10⁻³ m·K

1st law

ΔU = Q − W

Isothermal W

nRT ln(V₂/V₁)

Adiabatic

PVᵞ = const; TVᵞ⁻¹ = const

Carnot η

1 − T_c/T_h

Refrigerator COP

T_c/(T_h − T_c)

P

⅓ ρ v_rms²

v_rms

√(3RT/M)

v_avg

√(8RT/πM)

v_mp

√(2RT/M)

Mean KE (per molecule)

3/2 kT

x(t)

A sin(ωt+φ)

T (spring)

2π√(m/k)

T (pendulum)

2π√(L/g)

Energy

½kA²

v at x

ω√(A²−x²)

Wave

v = fλ

String

v = √(T/μ)

Sound in gas

v = √(γP/ρ)

Beat freq

|f₁ − f₂|

Doppler

f' = f(v ± v_o)/(v ∓ v_s)

Coulomb

F = kq₁q₂/r²

E of point charge

kq/r²

E of infinite sheet

σ/2ε₀

E inside conductor

0

Potential

V = kq/r

Dipole moment

p = q(2a)

E on axis (dipole)

2kp/r³

E ⟂ dipole

kp/r³

U (dipole in E)

−p·E

Parallel plate

C = ε₀A/d

With dielectric

C' = KC

Series

1/C = 1/C₁ + 1/C₂

Parallel

C = C₁ + C₂

Energy

U = ½CV² = Q²/2C

Ohm

V = IR

Resistivity

ρ = RA/L

Drift v

v_d = I/(nAe)

Power

VI = I²R = V²/R

Kirchhoff

ΣI = 0 (node); ΣV = 0 (loop)

Wheatstone (balance)

P/Q = R/S

Terminal V

ε − Ir

Lorentz

F = q(v × B)

Force on wire

F = IL × B

Biot–Savart

dB = μ₀/4π · IdL sinθ/r²

B (long wire)

μ₀I/(2πr)

B (loop centre)

μ₀I/(2R)

B (solenoid)

μ₀nI

Cyclotron radius

r = mv/(qB)

Torque on loop

τ = NIAB sinθ

Flux

Φ = B·A

EMF

ε = −dΦ/dt

Self L emf

ε = −L dI/dt

U (inductor)

½LI²

X_L

ωL

X_C

1/ωC

Z (RLC)

√(R² + (X_L − X_C)²)

Resonance ω

1/√(LC)

Transformer

V_s/V_p = N_s/N_p

Mirror

1/v + 1/u = 1/f

Lens

1/v − 1/u = 1/f

Magnification (lens)

m = v/u

Lensmaker

1/f = (n−1)(1/R₁ − 1/R₂)

Combination

1/F = 1/f₁ + 1/f₂ − d/(f₁f₂)

Power

P = 1/f(m)

Prism min dev

n = sin((A+D)/2)/sin(A/2)

Microscope M

L/f_o · (1 + D/f_e)

Telescope M

−f_o/f_e

Photon E

hν = hc/λ

KE_max

hν − φ

Stopping V

eV₀ = KE_max

de Broglie

λ = h/p = h/√(2mKE)

For electron (V volts)

λ = 12.27/√V Å

Bohr radius

rₙ = 0.529 n²/Z Å

Energy (H)

Eₙ = −13.6/n² eV

Rydberg

1/λ = R(1/n₁² − 1/n₂²)

Mass–energy

E = Δm·c²

Decay

N = N₀ e⁻λt

Half-life

t₁/₂ = 0.693/λ