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

[ Angle to Radius ]

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 v²_max

[ 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 ]

V_rms =	V_o

I_rms =	I_o

C

=

Q

/

V

[ Capacitance ]

C

=

A

ε₀

/

d

[ Parallel Plate Capacitor ]

w

=

½

C

V²

[ Energy in Capacitor ]

V_i	=	N_p

V_o		N_s

[ Transformer ]