Position: \(\vec{r}(t)=r\hat{r}\)
Angular Velocity: \(\vec{\omega}=\omega_z \hat{k}\)
Component of the Angular Velocity along the axis of rotation: \(\omega_z=\dfrac{d\theta}{dt} \)
Velocity: \(\vec{v}=r\dfrac{d\theta}{dt}\hat{\theta} \)
Angular Acceleration: \(\vec{\alpha} = \alpha_{z}\hat{k} \)
Component of the Angular Acceleration: \(\alpha_z=\dfrac{d\omega_z}{dt}=\dfrac{d^2\theta}{dt^2}\)
Acceleration: \(\vec{a}=a_r\hat{r}+a_{\theta}\hat{\theta} \)
\(a_r = -\frac{v^2}{r} = -r(\dfrac{d\theta}{dt})^2, a_{\theta} = r\dfrac{d^2\theta}{dt^2}= r\alpha_z\)
