Question

A long, thin rod of length l and mass m hangs from a pivot point about which it is free to swing in a vertical plane like a simple pendulum. Calculate the total angular momentum of the rod about the pivot point as a function of its instantaneous angular frequency ω. Calculate the total kinetic energy of the rod.

Answer 1

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Given that,

Instantaneous angular frequency

Mass of the rod

Length of the rod

We know that, Moment of inertia of the rod about a axis at the end of the rod is given by,

Therefore, total angular momentum of the rod about the pivot point is given by,

Also, Total kinetic energy of the rod is given by,

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