Mechanics formulae

Linear motion

\( \pmb{V = \frac{S}{t}} \) - Speed

\( \pmb{x = x_0 + vt} \) - Equation of motion

Accelerated linear motion

\( \pmb{a = \frac{V - V_0}{t}} \) - Acceleration

\( \pmb{S = V_0 t + \frac{at^2}{2}} \) - Displacement

\( \pmb{V = V_0 + at} \) - Velocity equation

Free fall

\( \pmb{h = V_0 t + \frac{at^2}{2}} \) - Height

\( \pmb{V = \sqrt{2gh}} \) - Final velocity

Kinematics

\( \pmb{a_c = \frac{v^2}{r}} \) - Centripetal acceleration

\( \pmb{F_c = \frac{mv^2}{r}} \) - Centripetal force

Dynamics

\( \pmb{F = ma} \) - Newton's second law

\( \pmb{F_{1,2} = -F_{2,1}} \) - Newton's third law

\( \pmb{F_e = k \Delta x} \) - Hooke's law

\( \pmb{F_f = \mu N} \) - Friction force

\( \pmb{F_g = G \frac{m_1 m_2}{r^2}} \) - Gravitational force

Statics

\( \pmb{M = Fd} \) - Moment of force

\( \pmb{P = \frac{F}{A}} \) - Pressure

\( \pmb{P = \rho gh} \) - Hydrostatic pressure

\( \pmb{F_A = \rho_f g V} \) - Archimedes' force

Work energy power

\( \pmb{A = F s \cos{\alpha}} \) - Work

\( \pmb{E_k = \frac{mv^2}{2}} \) - Kinetic energy

\( \pmb{E_p = mgh} \) - Potential energy

\( \pmb{P = \frac{A}{t}} \) - Power

Momentum

\( \pmb{p = mV} \) - Momentum

\( \pmb{m_1 V_1 + m_2 V_2 = m_1 V'_1 + m_2 V'_2} \) - Conservation of momentum

\( \pmb{H = F \Delta t} \) - Force momentum