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A tapered cup rolled on a flat surface makes a circular path. What does this tell you about the tangential speed of the rim of the wide end of the cup compared with that of the rim of the narrow end?

User George
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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.

User MivaScott
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