Question

An automobile tire has a radius of 0.307 m, and its center moves forward with a linear speed of v=23.1 m/s. (a) Determine the angular speed of the wheel. (b) Relative to the axle, what is the tangential speed of a point located 0.237 m from the axle?

Answer 1

The angular speed of the wheel is approximately 75.2 rad/s. The tangential speed of a point 0.237 m from the axle is approximately 17.82 m/s relative to the axle.

Step-by-step explanation:

To solve for the angular speed of the wheel, we can use the relationship that linear speed v is equal to the angular speed ω times the radius r of the wheel (v = rω). Given the linear speed v = 23.1 m/s and the radius r = 0.307 m, we can rearrange the equation to solve for ω = v / r. Substituting the given values, the angular speed ω is approximately 75.2 rad/s.

For part (b), to find the tangential speed at a point 0.237 m from the axle, we use the same relationship v = rω. The tangential speed at this new radius is simply 0.237 m multiplied by the angular speed we found earlier (75.2 rad/s), yielding a tangential speed of approximately 17.82 m/s relative to the axle.