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Physical pendulum
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A rigid body swinging about a pivot.
T = 2π√(I/mgd)A rigid body pivoted at distance d from its centre of mass has T = 2π√(I/mgd) with I about the pivot. The equivalent length is I/md.
A uniform rod pivoted at its end: T = 2π√(2L/3g).
Use I about the pivot.
In more detail
A physical pendulum is any rigid body that swings about a pivot. Its period is T = 2π sqrt(I/(mgd)), where I is the moment of inertia about the pivot and d is the distance from the pivot to the centre of mass.
Real-world uses
- Engineers measure moments of inertia by timing the swing of a body.
- Grandfather clock pendulums are physical pendulums with a bob and a rod.
- A metre stick pivoted at one end swings like a physical pendulum, and its period depends on where it is pivoted.
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Frequently asked questions
How is it different from a simple pendulum?
It uses the body's moment of inertia, not a point mass on a string.
Can I measure g with a physical pendulum?
Yes, if you know the moment of inertia and the pivot distance.
How is a physical pendulum different from a simple one?
Its mass is spread out, so the moment of inertia about the pivot and the position of its centre of mass both matter.
Related topics in Oscillations & SHM
Simple pendulum · Small-angle approximation · Pendulum at large amplitude · Torsional pendulum · Second's pendulum · Simple pendulum in elevator