Q.A wheel starts from rest and is given a constant angular acceleration of $2\ \text{rad/s}^2$ until it reaches an angular velocity of $20\ \text{rad/s}$. Find the total angle turned through during this time, and the number of complete revolutions made.

Using the rotational kinematic equation $\omega^2 = \omega_0^2 + 2\alpha\theta$, with $\omega_0=0$ (starts from rest), $\omega=20\ \text{rad/s}$, $\alpha=2\ \text{rad/s}^2$:

$20^2 = 0 + 2(2)\theta \quad\Longrightarrow\quad 400 = 4\theta \quad\Longrightarrow\quad \theta = 100\ \text{rad}$ …

Apply $\omega^2=\omega_0^2+2\alpha\theta$ to find $\theta$ in radians, then divide …

• Reporting the answer in radians as though it were already the number of revolutions.
• Using $\theta=\omega t$ without first finding the (unknown) time $t$, instead of the more dire …