## Motion

#### Average Speed

*v* = *d/t*

#### Average Velocity

*v̅* = Δ*x*/Δ*t*

#### Average Acceleration

*a̅* = Δ*v̅*/Δ*t*

#### Translational motion at constant acceleration

*x - x*_{0} = *v*_{0}t + ½*at*^{2}

*v - v*_{0} = *at*

*v*^{2} = *v*_{0}^{2} + 2*a*(*x - x*_{0}) becomes *v* = √2*gh* in free fall where *v*_{0} = 0

*v̅* = ½(*v* + *v*_{0})

## Force

#### Newton's Second Law

*F* = *ma*

#### Gravity

*F*_{g} = *G*(*m*_{1}m_{2})/*r*^{2}

#### Inclined Planes

*F*_{N} = *mg* cos θ

*F*_{incline} = *mg* sin θ

#### Friction

*F*_{fr} = μ_{k}*F*_{N} ≤ μ_{s}*F*_{N}

#### Hooke's Law

*F* = -*k*Δ*x*

#### Torque

τ = *Fl*

#### Equilibrium

*F*_{direction} = *F*_{opposite direction} at equilibrium

τ_{clockwise} = τ_{counter clockwise} at equilibrium

*F*_{direction} = *F*_{opposite direction} ± *ma* at non-equilibrium

## Energy

#### Kinetic energy

*K* = ½*mv*^{2}

*
*#### Potential energy

*U*_{g} = *mgh*

*U*_{e} = ½*k*Δ*x*^{2}

#### Conservation of energy

*E*_{total} = *E*_{KE} + *E*_{PE}

*PE*_{1} + *KE*_{1} = *PE*_{2} + *KE*_{2}

#### Work-energy theorem

*W* = Δ*K* + Δ*U* + Δ*E*_{i}

#### Rest mass energy

*E* = *mc*^{2}

#### Work

*W* = *Fd*cosθ

*W* = Δ*K* + Δ*U* + Δ*E*_{i}

#### Power

*P* = *Fv*cosθ

*P* = Δ*W* / Δ*t*

## Fluids

#### Density

ρ = *m*/*V*

#### Buoyant Force

*F*_{buoyant} = ρ*Vg*

#### Hydrostatic pressure

*P* = ρ*gh*

#### Continuity equation

*A•v* = constant

#### Bernoulli’s equation

*p* + ρ*gy* + ½ρ*v*^{2} = constant

## Electricity and Magnetism

#### Coulomb’s Law

*F* = *k* (*Q*_{1}Q_{2}/*r*^{2})

#### Electric field due to a point charge

*E* = *k* (*Q/r*^{2})

#### Electric potential energy

*U* = *k* (*Q*_{1}Q_{2}/r)

#### Electric potential

*V* = *k* (*Q/r*)

#### Constant Electric Fields

*F* = *qE*

*V* = *Ed*

*U* = *qEd*

*U* = *Vq*

#### Ohm's Law

*I* = *V/R*

#### Resistivity

ρ = *R•A/L*

#### Resistors

*R*_{eff} = *R*_{1} + *R*_{2} + ... in series

1/*R*_{eff} = 1/*R*_{1} + 1/*R*_{2} + ... in parallel

#### Capacitors

1/*C*_{eff} = 1/*C*_{1} + 1/*C*_{2} + ... in series

*C*_{eff} = *C*_{1} + *C*_{2} + ... in parallel

#### Force on a charge moving in a magnetic field

*F* = *qvB* sin θ

## Waves, Sound, and Light

#### Wave velocity

*v* = *f*λ

#### Wave period

*T* = 1/*f*

#### Beat frequency

*f* = |*f*_{1} - f_{2}|

*
*#### Doppler effect

Δ*f*/*f*_{s} = *v/c*

Δ*λ*/*λ*_{s} = *v/c*

#### Photon energy

*E* = *hf*

#### Snell's Law

*n*_{1} sin θ_{1} = *n*_{2} sin θ_{2}

#### Lens equation

1/*p* + 1/*q* = 1/*f*