Answer to Question #104553 in Physics for Gitgud

Question

a tire 0.500m in radius rotates at a constant rate od 200 rev/mon. Find the speed and acceleration of a small stone lodged in the tread of the tire (on its outer edge)

Answer 1

Given:

$R=0.500\:\rm m;$

$n=200\:\rm rev/min.$

The angular velocity

$$\omega=2\pi n=2\pi\times 200=1256\:\rm rad/min=20.9\:\rm rad/s.$$

The linear speed

$$v=\omega R=20.9\times 0.500=10.45\:\rm m/s.$$

The acceleration

$$a=\omega^2R=20.9^2\times 0.500=218\:\rm m/s^2.$$