Question

Consider a tire with a diameter of d (and therefore with a radius of r) which is on a car traveling at a constant speed of v on a level road in the positive direction of the x-axis. The car is passing a hitchhiker sitting near the road. Relative to a woman in the car, what is the x velocity of the center of the wheel? Also relative to a woman in the car, what is the x velocity for a point at the top of the tire? Finally, relative to a woman in the car, what is the x velocity for a point at the bottom of the tire?

Answer 1

Relative to a woman in the car, the x velocity of the center of the wheel is zero, the x velocity for a point at the top of the tire is twice the car's speed, and the x velocity for a point at the bottom of the tire is zero.

Step-by-step explanation:

The question involves understanding the concept of relative velocity in mechanics, a branch of physics. Specifically, we are analyzing the motion of different points on a rotating tire of a car that is moving at a constant velocity in terms of a person sitting inside the car. Firstly, the x velocity of the center of the wheel, relative to a woman in the car, is zero since both the center of the wheel and the woman are moving together. Secondly, for a point at the top of the tire, the x velocity relative to the woman in the car is twice the car's speed (2v); this is because the tangential velocity of the top of the tire adds to the linear velocity of the car. Lastly, the x velocity for a point at the bottom of the tire relative to the woman in the car is zero since it is momentarily at rest with respect to the road and thus also relative to the woman in the car. This analysis assumes the tire is not slipping on the road.