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
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
| Material | Coefficients of friction |
|---|---|
| Aluminium | 0.61 |
| Rubber | 1.0 |
| Wood | 0.62 |
| Glass | 0.94 |
