Uniform circular motion and circular motion with constant angular acceleration
Angular position, angular speed and angular acceleration in uniform circular motion
The same way as with uniform motion, we can easily determine the kinematic quantities describing uniform circular motion:
- angular position: \(\phi(t) = \phi_0 + \omega t,\) where \(\phi_0\) is the initial angular position;
- angular speed: \(\omega = \mathrm{const};\)
- angular acceleration: \(\alpha = 0.\)
Angular position, angular speed and angular acceleration in circular motion with constant angular acceleration
Using the analogy with linear motion with constant acceleration, we can define the kinematic quantities describing circular motion with constant angular acceleration:
- angular position: \(\phi(t) = \phi_0 + \omega_0 t + \frac{\alpha}{2} t^2,\) where \(\phi_0\) is the initial angular position and \(\omega_0\) is the initial angular speed;
- angular speed: \(\omega = \omega_0 + \alpha t;\)
- angular acceleration: \(\alpha = \mathrm{const}.\)