Question

A wheel 200mm in diameter coasts to rest from a speed of 800rpm in 600 seconds. Determine the angular acceleration?

Answer 1

$$\alpha=\dfrac{\omega-\omega_0}{t},$$ $$\alpha=\dfrac{0-800\ \dfrac{rev}{min}\cdot\dfrac{1\ min}{60\ s}\cdot\dfrac{2\pi\ rad}{1\ rev}}{600\ s}=-0.14\ \dfrac{rad}{s^2}.$$

The sign minus means that the wheel decelerates.