College Physics II – Mechanics, Sound, Oscillations, and Waves
Definition
A physical pendulum is a rigid body that oscillates about a pivot point, where the mass distribution of the body affects its oscillatory motion. Unlike an ideal simple pendulum, its period depends on the shape and mass distribution.
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The period of a physical pendulum is given by $T = 2\pi \sqrt{\frac{I}{mgh}}$, where $I$ is the moment of inertia about the pivot point, $m$ is the mass, $g$ is the acceleration due to gravity, and $h$ is the distance from the pivot to the center of mass.
For small angular displacements, a physical pendulum exhibits simple harmonic motion.
The effective length of a physical pendulum is defined as $L_{eff} = \frac{I}{mh}$.
The restoring torque for a physical pendulum is given by $\tau = -mgh \sin(\theta)$, where $\theta$ is the angular displacement.
Increasing the distance between the pivot point and the center of mass increases the period of oscillation.
Review Questions
What factors affect the period of a physical pendulum?
How does one calculate the effective length ($L_{eff}$) of a physical pendulum?
Describe how small angular displacements impact a physical pendulum's motion.
Related terms
Moment of Inertia: A measure of an object's resistance to changes in its rotation rate, dependent on mass distribution relative to an axis.
Simple Harmonic Motion: Type of periodic motion where restoring force is directly proportional to displacement and acts in opposite direction.
Torque: A force that causes rotation around an axis; calculated as force multiplied by perpendicular distance from axis.