Creative Commons License Copyright © Michael Richmond. This work is licensed under a Creative Commons License.

The pendulum-peg problem (part I)

Consider the following experiment

A ball of mass m is attached to a string of length L, and is pulled so that the ball is an initial height D from the lowest point in its swing. A rod is clamped at a height h above the lowest point so that when the pendulum swings down, the string wraps around the rod, and the ball swings around in a circle of smaller radius.

Your challenge:

Determine the smallest height D from which the ball can be released in order that it complete the small circle without the string going slack.

Creative Commons License Copyright © Michael Richmond. This work is licensed under a Creative Commons License.