Question

A rolling wheel of diameter of 68 cm slows down uniformly from 8.4 m/s to rest over a distance of 115 m. What is the magnitude of its angular acceleration if there was no slipping?

Answer 1

We have angular acceleration

\(\alpha=\frac{a}{R}\)

We have

\(\begin{aligned} v^{2} &=u^{2}+2 a s \\ u &=0 \\ v^{2} &=2 a s \\ a &=\frac{v^{2}}{2 s} \\ &=\frac{8.4^{2}}{2 \times 115} \\ &=0.306 \\ \alpha &=\frac{0.306}{0.34} \\ &=0.902 \mathrm{rad} / \mathrm{s} \end{aligned}\)