A wheel of radius R is rolling on a horizontal surface. Its center is moving forward with speed v. A point on the wheel a distance r/3 below the center is moving forward at a speed 2v/3. The wheel is
A) rolling without slipping.
B) not rotating at all.
C) made of rubber.
D) slipping because its angular speed is too low to be rolling without slipping.
E) slipping because its angular speed is too high to be rolling without slipping.

Question

Quizplus · Accepted Answer

For a wheel to roll without slipping, the speed of the center of the wheel (v) must be equal to the product of the angular speed and the radius (ωR). 
Since the point on the wheel a distance r/3 below the center has a speed of 2v/3, we know that its angular speed is 2v/3 divided by (r/3), which simplifies to 2v/r. 
To check if the wheel is rolling without slipping, we can compare v and ωR. 
v = ωR 
2v/3r * r = v 
2v/3 = v 
Therefore, the wheel is rolling without slipping, and the answer is A.

A Wheel of Radius R Is Rolling on a Horizontal