Chapter 10, Problem 7A

When you roll a cylinder across a surface it follows a straight-line path. A tapered cup rolled on the same surface follows a circular path. Why?

To determine

The reason for the circular path followed by the tapered cup.

Explanation of Solution

Introduction:

For a solid body rotating, the entire body rotates with the same angular speed. The body rotates through the same angle during the same interval of time.

A cylinder rolling on a surface travels in a straight line because it is symmetrical, both the ends travel same distance per revolution. But a tapered cup travels in a circular path because the wider part of the cup travels greater distance per revolution than the tapered end.

Conclusion:

A tapered cup travels in a circular path because the wider part of the cup travels greater distance per revolution than the tapered end.