Question

An automobile tire has a radius of 0.315 m, and its center moves forward with a linear speed of v = 19.3 m/s. (a) Determine the angular speed of the wheel. (b) Relative to the axle, what is the tangential speed of a point located 0.193 m from the axle?

Answer 1

• angular speed: 61.3 radians/s
• tangential speed at .193 m: 11.8 m/s

Explanation:

The forward speed of the center of the tire with respect to the ground is the same as the tangential speed of the tire at its full radius of 0.315 m, relative to the axle.

The angular speed of the tire is the ratio of tangential speed to radius:

(19.3 m/s)/(0.315 m) ≈ 61.27 radians/s

The tangential speed at any other radius is the product of angular speed and radius. At a radius of 0.193 m, the tangential speed is ...

(0.193 m)×(19.3 m/s)/(0.315 m) ≈ 11.825 m/s ≈ 11.8 m/s