# Formulas

Mechanics
v = u + a t

 s = u t + ½ a t 2
 v 2 = u 2 + 2 a s
[ Linear Motion Equations ]
F = m a [ Force v Acceleration ]
m1u1 + m2u2 = m1v1 + m2v2
[ Momentum ]
Θ = s / r
Ω = Θ / t [ Angular Velocity ]
v = r / ω [ Linear Vel → Angular Vel ]
a = r ω 2 = v 2 / r [ Centripetal Acceleration ]
F = m r ω 2 = m v 2 / r [ Centripetal Force ]
w = mg [ Weight ]
 F = G m1 m2 d 2
[ Newton’s Law of Gravitation ]
 g = G M r 2
[ g – Gravitation Constant ]
 T 2 = 4 π 2 r 3 G M
[ Period v Distance 3 ]
ρ = m / v [ Density ]
P = Force / Area = ρ g h [ Pressure ]
T = F d [ Moment /Couple ]
F = – k s [ Hooke’s Law ]
a = – ω2 s [ Simple Harmonic Motion ]
T = 1 / f = 2 λ / ω [ Period ]
 T = 2 π [ Simple Pendulum ]
W = F d [ Work = Force x distance ]
P = W / t [ Power = Work / time ]

Heat

Q = m c ΔΘ [ Specific Heat Capacity ]
Q = m l [ Specific Latent Heat ]

Modern Physics

E = h f [ Energy of Photon ]

h f = Φ + ½ m v2max [ Photoelectric Equation ]
Rate of decay = λ N [ Rate of decay ] = ln 2 λ
[ Half-life ]
E = m c2 [ Mass – Energy ]
Sound/Light
c = f λ [ Velocity of Wave ]
f
=
 f c c u
[ Doppler effect ]
 f = 1  2 l
[ Fundamental Frequency]
1 / f = 1 / u + 1 / v [ Mirrors/lens equation ]
m = v / u [ Magnification ]
P = 1 / f [ Power of Lens ]
P = P 1 + P 2 [ Combination of lens ]
n = sin i / sin r [ Refractive Index ]
n = 1 / sin C [ Refractive Index ]
n λ = d sin Θ [ Diffraction Grating ]

Electricity

 F = Q 1 Q 2 4 π ε0 d2
[ Coulomb’s law ]
E = F / Q [ Electric Field Strength ]
V = W / Q [ Potential Difference ]
V = I R [ Potential Difference ]
ρ = R A / l [ Resistivity ]
R = R1 + R2 [ Resistors in Series ]
 1 = 1 + 1   R R1 R2
[ Resistors in Parallel ]
 R1 = R3  R2 R4
[ Wheatstone Bridge ]

 E = l2 R
[ Joule’s Law ]
P = V I [ Power ]
 F = B I l
[ Force on a conductor ]
F = q v B [ Force on a charge particle ]
Φ = B A [ Magnetic Flux ]
 E = – d Φ dt
[ Induced emf ]
 Vrms = Vo  Irms = Io  C = Q / V
[ Capacitance ]
 C = A ε0 / d
[ Parallel Plate Capacitor ]
 w = ½ C V2
[ Energy in Capacitor ]
 Vi = Np  Vo Ns
[ Transformer ]