Newton's Second Law: $\vec{F}_{net} = m\vec{a} = \frac{d\vec{p}}{dt} \quad [M^1L^1T^{-2}] \quad \text{(N)}$

Linear Momentum: $\vec{p} = m\vec{v} \quad [M^1L^1T^{-1}] \quad \text{(kg·m/s)}$

Impulse: $\vec{J} = \vec{F}\,\Delta t = \Delta\vec{p} \quad [M^1L^1T^{-1}] \quad \text{(N·s)}$

Apparent Weight in Lift: $W' = m(g \pm a) \quad [M^1L^1T^{-2}] \quad \text{(N)}$

Atwood Machine: $a = \frac{(m_1 - m_2)\,g}{m_1 + m_2} \quad [M^0L^1T^{-2}] \qquad T = \frac{2m_1 m_2\,g}{m_1 + m_2} \quad [M^1L^1T^{-2}]$

Friction: $0 \leq f_s \leq \mu_s N \qquad f_k = \mu_k N \qquad f_r = \mu_r N \qquad \mu \text{ is dimensionless}$

Angle of Repose: $\tan\theta_{repose} = \mu_s \quad \text{(dimensionless)}$

Inclined Plane: $N = mg\cos\theta \quad [M^1L^1T^{-2}] \qquad F_{\parallel} = mg\sin\theta \quad [M^1L^1T^{-2}]$

Centripetal Force: $F_c = \frac{mv^2}{r} \quad [M^1L^1T^{-2}] \quad \text{(N)}$

Maximum Speed on Level Road: $v_{max} = \sqrt{\mu r g} \quad [M^0L^1T^{-1}] \quad \text{(m/s)}$

Banking Angle (no friction): $\tan\theta = \frac{v^2}{rg} \quad \text{(dimensionless)}$