# List of formulas related to Dynamics

## Straight line motion

s: distance(m), t: time (s, second), v: velocity (m/s), VA: average velocity

$$V = \frac{S}{T}$$ $$V_A = \frac{S_1 + S_1 + .... + S_N}{T_1 + T_1 + .... + T_N}$$ ### Constant Acceleration Straight Line Motion

A: Acceleration, V0: Initial Velocity, V: Velocity At Time T

$$A = \frac{V - V_0}{T}(M/S^2)$$ $$S = V_0 T + \frac{1}{2}AT^2$$ $$v^2 -v_0 ^2 = 2as$$

#### Distance Function

X0: Initial Distance From Origin, X: Distance At Time T

$$x = x_0 + v_0 t + \frac{1}{2}(at^2)$$

#### Uniform Circular Motion

Ø: angle (radian), l: length of an arc, R: radius of circle, ω: angular velocity (rad/s), t: time the object moves a length of l

$$\phi = \frac{1}{R}$$ $$\omega = \frac{v}{R}$$ $$v^2 -v_0 ^2 = 2as$$ $$v = \frac{1}{t} = \omega R$$

#### Centripetal Force

f: frequency (Hz), T: the period for one rotation (s), a: centripetal acceleration, F: centripetal force (N, Newton)

$$f = \frac{1}{T}$$ $$a = \frac{v^2}{R} = \omega ^2 R$$ $$F = ma = m \frac{v^2}{R}$$ #### Constant Acceleration Circular Motion

γ: angular acceleration

$$\omega = \omega _0 + \gamma t$$ $$\phi = \phi _0 + \omega t + \frac{1}{2} \gamma t^2$$ $$\omega ^2 - \omega _0 ^2 = 2 \gamma \phi$$

#### Acceleration

at : tangential acceleration, an : normal acceleration

$$a_t = R \gamma$$ $$a_n = R \omega ^2 = \frac{v^2}{R}$$

#### Freely Falling From Height H

g: gravitational acceleration, v: velocity at t, s: distance after t, vh: velocity when touching the ground, th: time to touch down

$$a = g$$ $$v = gt$$ $$v_h = \sqrt{2gh}$$ $$s = \frac{1}{2} gt^2$$ $$t_h = \sqrt{\frac{2h}{g}}$$ g=9.8m/s2

#### Vertical Projectile Motion

Hmax : maximum height, v0: initial velocity

$$h_{max} = \frac{v _0 ^2}{2g}$$ $$a = -g$$

Motion equation and velocity equation

$$y = - \frac{1}{2} gt^2 + v_0 t$$ $$v^2 - v _0 ^2 = 2gh$$ $$v = v_0 - gt$$ #### Angled Projectile Motion

vx, vy: velocity; x, y: motion equation by t; H: maximum height; L: maximum distance

$$v_{x} = v_0 \cos \alpha$$ $$v_{y} = v_0 \sin \alpha - gt$$ $$x = (v_0 \sin \alpha)t$$ $$y = (v_0 \sin \alpha)t - \frac{1}{2}gt^2$$ $$H = \frac{v _0 ^2 \sin ^2 \alpha}{2g}$$ $$L = \frac{v _0 ^2 \sin 2 \alpha}{2g}$$ #### Horizontal Projectile Motion

th: time when touchdown, vh: velocity when touchdown

$$v_{x} = v_0$$ $$v_{y} = - gt$$ $$x = v_0 t$$ $$y = h - \frac{1}{2}gt^2$$ $$h = 0 \Rightarrow t_h =\frac{2h}{g}$$ $$v_h = \sqrt{ v _x ^2 + v _y ^2} = \sqrt{ v _0 ^2 + (gt ^2)}$$ #### Sliding Motion On An Inclined Plane

µ: coefficient of some materials

$$a = g(sin \alpha - sin \alpha)$$

Fiction coefficient of some materials

MaterialCoefficients of friction
Aluminium0.61
Rubber1.0
Wood0.62
Glass0.94 