## Rotational Motion

 $r$ $\mathrm{r}$ radius $\varphi$ $\mathrm{rad}$ angle in radians $\omega$ $\mathrm{s^{-1}}$ angular velocity $\alpha$ $\mathrm{s^{-2}}$ angular acceleration $t$ $\mathrm{s}$ time $T$ $\mathrm{s}$ period, duration of a rotation $f$ $\mathrm{s^{-1}, Hz}$ revolution frequency $n$ $\mathrm{s^{-1}}$ rotational speed

### Uniform Rotation

 Condition: $\omega = \mathrm{const.}$

$$\varphi = \omega \, t + \varphi_0$$

$$\omega = \frac{2 \,\pi}{T} = 2 \,\pi \, f \qquad n = \frac{1}{T}$$

### Uniformly accelerated Rotation

 Condition: $\alpha = \mathrm{const.}$

$$\varphi = \frac{\alpha}{2} \, t^2 + \omega_0 \, t + \varphi_0$$

### Rotation in general

$$\varphi = \int\limits_{t_1}^{t_2}\! \omega(t)\;\mathrm{d}t$$

$$\omega = \int\limits_{t_1}^{t_2}\! \alpha(t)\;\mathrm{d}t \qquad \omega = \frac{\mathrm{d} \varphi}{\mathrm{d}t} = \varphi'(t) = \dot{\varphi}$$

$$\alpha = \frac{\mathrm{d} \omega}{\mathrm{d}t} = \omega'(t) \qquad \alpha = \frac{\mathrm{d^2} \varphi}{\mathrm{d}t^2} = \ddot{\varphi}$$