### Physics Formulas - Mechanics

#### Kinematics Formulas

The**Kinematic Equations**apply to one-dimmensional motion with costant acceleration from point 1, situated d

_{1}from a point of reference to point 2, situated d

_{2}from the same point of reference. v

_{1}is the velocity at point 1 and v

_{2}is the velocity at point 2.

v

_{2}= v

_{1}+ a·t

d

_{2}= d

_{1}+ (v

_{1}+ v

_{2})·t/2

d

_{2}= d

_{1}+ v

_{1}·t + a·t

^{2}/2

d

_{2}= d

_{1}+ v

_{2}·t - a·t

^{2}/2

v

_{2}

^{2}= v

_{1}

^{2}+ 2a(d

_{2}- d

_{1})

Average velocity: v

_{av}= Δd/Δt

Average acceleration: a

_{av}= Δv/Δt

**Rotational kinematics**equations with constant angular acceleration:

ω

_{2}= ω

_{1}+ α·t

Φ

_{2}= Φ

_{1}+ (ω

_{1}+ ω

_{2})·t/2

Φ

_{2}= Φ

_{1}+ ω

_{1}·t + α·t

^{2}/2

Φ

_{2}= Φ

_{1}+ ω

_{2}·t - α·t

^{2}/2

ω

_{2}

^{2}= ω

_{1}

^{2}+ 2α(Φ

_{2}- Φ

_{1})

Average angular velocity: ω

_{av}= Δθ/Δt

Average angular acceleration: α

_{av}= Δω/Δt

Frequency: f = ω/2π

Period: T = 2π/ω

**Relations between angular and linear variables:**

l = Φ·r

v = ω·r

a = α·r

#### Dynamics Formulas

Pressure: P = F/ANewton's Second Law: F = m·a

Force of kinetic friction: F

_{f}= μ·N

Hooke's Law: F = -k·x

Centripetal Force: F

_{c}= m·v

^{2}/R

Centripetal acceleration: a

_{c}= v

^{2}/R

#### Work, Energy, Conservation Laws Formulas

Work: W = F · d = Fdcos(α)Potential Energy: PE = m·g·h

Kinetic Energy: KE = m·v

^{2}/2

Mechanical Energy: E = KE + PE

Instantaneous Power: P = F·v

The Work-Energy Theorem: W = ΔKE

#### Gravitation Formulas

Newtonian gravity formula: F_{g}= G·m·M/R

^{2}

Kepler's Third Law: T

^{2}/a

^{3}= ct.

### Physics Formulas - Electricity and Magnetism

#### Electric Fields and Forces Formulas

Coulomb's Law: F = k·q_{1}·q

_{1}/r

^{2}

Electric field of a charge q: E = k·q/r

^{2}

Work done by electric field: W = q·E·d

Electric field between two metallic plates: E = V/d

#### DC Circuits Formulas

Ohm's Law: V = I·RPower dissipated in a resistor: P = I·V = V

^{2}/R = R·I

^{2}

Resistance: R = ρ·l/A

Equivalent resistance of series resistors: R

_{s}= R

_{1}+ R

_{2}+...

Equivalent resistance of parallel resistors: 1/R

_{p}= 1/R

_{1}+ 1/R

_{2}+...

Equivalent capacitance of series capacitors: 1/C

_{s}= 1/C

_{1}+ 1/C

_{2}+...

Equivalent capacitance of parallel capacitors: C

_{p}= C

_{1}+ C

_{2}+...

#### Magnetic Fields and Forces Formulas

Magnetic force on a moving charge: F = q(v x B) = q·v·B·sin(θ)Magnetic force on a current carrying wire: F = I·l·B·sin(θ)

Magnetic field created by a current: B = (μ

_{o}/2π)·(I/r)

Faraday's Law: E = -dΦ/dt

### Physics Formulas - Thermodynamics

Heat added or emoved: Q = m·c·ΔTChange in Internal Energy: ΔU = Q - W

Boyle's Law: P

_{1}V

_{1}= P

_{2}V

_{2}

Charles's Law: V

_{1}/T

_{1}= V

_{2}/T

_{2}

Efficiency of a heat engine(%): E = (W/Q

_{hot})·100

### Physics Formulas - Waves and Optics

Snell's Law: n_{1}·sin(θ

_{1}) = n

_{2}·sin(θ

_{2})

Wave speed: v = λ·f

Velocity of light: v = c/n

Magnification: m = -d

_{i}/d

_{o}

Law of Reflection: θ

_{reflection}= θ

_{incidence}

Mirror and lens equation: 1/d

_{1}+ 1/d

_{1}= 1/f

### Physics Formulas - Modern Physics

The energy of a photon: E = h·fMatter wavelength: λ = h/p

Relativistic factor: γ

^{2}= 1/(1 - v

^{2}/c

^{2})

De Broglie Wavelength: λ = h/(mv)

Half life of radioactive material: T

_{half}= ln(2)/λ

Mass energy equivalence: E = m

_{o}·c

^{2}