Equations of Motion (constant acceleration)

$v = u + at \quad [LT^{-1}] = [LT^{-1}] + [LT^{-2}][T]$

$s = ut + \tfrac{1}{2}at^2 \quad [L] = [LT^{-1}][T] + [LT^{-2}][T^2]$

$v^2 = u^2 + 2as \quad [L^2T^{-2}] = [L^2T^{-2}] + [LT^{-2}][L]$

$s_n = u + \frac{a(2n-1)}{2} \quad [L] = [LT^{-1}] + [LT^{-2}][T]$

Projectile Motion

$T = \frac{2u\sin\theta}{g} \quad [M^0L^0T^1] = \frac{[LT^{-1}]}{[LT^{-2}]}$

$H = \frac{u^2\sin^2\theta}{2g} \quad [M^0L^1T^0] = \frac{[L^2T^{-2}]}{[LT^{-2}]}$

$R = \frac{u^2\sin 2\theta}{g} \quad [M^0L^1T^0] = \frac{[L^2T^{-2}]}{[LT^{-2}]}$

$R_{max} = \frac{u^2}{g} \text{ at } \theta = 45°$

Vectors

$A_x = A\cos\theta, \quad A_y = A\sin\theta, \quad A = \sqrt{A_x^2 + A_y^2}$

$\vec{A}\cdot\vec{B} = AB\cos\theta \quad \text{(scalar)}$

$|\vec{A}\times\vec{B}| = AB\sin\theta \quad \text{(vector, direction by right-hand rule)}$

Circular Motion

$\omega = \frac{v}{r} \quad [M^0L^0T^{-1}] \text{ (rad/s)}$

$a_c = \frac{v^2}{r} = \omega^2 r \quad [M^0L^1T^{-2}] \text{ (m/s}^2\text{)}$