Question

A flywheel initially at rest accelerated uniformly at 6 rads-2. Calculate the angular velocity after 20 s and its angular displacement.

Answer 1

The angular velocity for the constanly accelerating (from the rest) body is given as follows:

$$\omega = \alpha t$$

where $\alpha = 6rad/s^2$ is the angular acceleration, and $t = 20s$ is the time. Thus, obtain:

$$\omega = 6\cdot 20 = 120\space rad/s$$

The angular displacement is:

$$\varphi = \dfrac{\alpha t^2}{2} = \dfrac{6\cdot 20^2}{2} = 1200 \space rad$$

Answer. Angular velocity: 120 rad/s, angular displacement: 1200 rad.