Two children are playing with a roll of paper towels. One child holds the roll between the index fingers of her hands so that it is free to rotate and the second child pills at constant speed on the free end of the paper towels. As the child pulls the paper towels, the radius of the roll of remaining towels decreases.
How does the torque on the roll change with time?

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Solution

This is a torque due to friction, and the magnitude depends on the normal force between the surfaces in contact. As the weight of the roll decreases the frictional force decreases leading to a decreasing torque.

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