A compound pendulum (or physical pendulum) is one where the rod is not massless, and may have extended size; that is, an arbitrarily shaped rigid body swinging by a pivot. In this case the pendulum's period depends on its moment of inertia I around the pivot point.
The equation of torque gives:
where:
- is the angular acceleration.
- is the torque
The torque is generated by gravity so:
where:
- L is the distance from the pivot to the center of mass of the pendulum
- θ is the angle from the vertical
Hence, under the small-angle approximation ,
This is of the same form as the conventional simple pendulum and this gives a period of:
And a frequency of:
Read more about this topic: Pendulum (mathematics)
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