Final answer:
The rim of the wide end of a tapered cup will have a greater tangential speed than the rim of the narrow end due to its larger radius, as the tangential speed is proportional to the radius for a constant angular velocity.
Step-by-step explanation:
When a tapered cup rolls on a flat surface, the path it takes is circular, revealing a difference in the tangential speed of the cup's rim between the wide and narrow ends. The equation v = rw, where v is the tangential speed, r is the radius from the center of rotation, and w is the angular velocity, tells us that for a constant angular velocity, the tangential speed is proportional to the radius. Thus, the rim of the wide end of the cup, having a larger radius, will have a greater tangential speed than the rim of the narrow end. Because the cup is tapered, the wide end travels a longer path in the same amount of time, which results in it moving faster to maintain the same angular velocity.