### 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/A

Newton'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·R

Power 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·ΔT

Change 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·f

Matter 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}