A sports utility vehicle has tires which are 110 cm in diameter.The tires rotate with a constant angular speed.A point on the tire that is 0.30 m from the center has a tangential speed of 2.0 m/s.What is the tangential speed of a point on the rim of the tire?

Question

Quizplus · Accepted Answer

The tangential speed $v$ of a point on a rotating object is directly proportional to its distance $r$ from the center of rotation, given by $v = r\omega$, where $\omega$ is the angular speed. Since the point 0.30 m from the center has a tangential speed of 2.0 m/s, any other point's tangential speed can be found by scaling this speed by the ratio of their distances from the center. The diameter of the tire is 110 cm (or 1.10 m), so the radius is 0.55 m. The tangential speed at the rim is $(0.55 m / 0.30 m) \times 2.0 m/s = 3.67 m/s$.

A Sports Utility Vehicle Has Tires Which Are 110 Cm