What is a simple pendulum?

An idealized point-mass bob suspended from a string of negligible mass and length $L$.

What is a physical pendulum?

A rigid extended object that oscillates about a fixed pivot under gravity.

What is the small-angle period of a physical pendulum?

$T=2\pi\sqrt{I/(mgd)}$, where $I$ is the moment of inertia about the pivot and $d$ is the pivot-to-center-of-mass distance.

What is a torsion constant?

The measure of a wire's or spring's twisting stiffness in the restoring-torque relation $\tau=-\kappa\theta$.

What is the small-twist period of a torsional pendulum?

$T=2\pi\sqrt{I/\kappa}$, where $I$ is rotational inertia about the axis and $\kappa$ is the torsion constant.

Classical mechanicsLesson 2 of 2 in the course Oscillations

Simple, Physical, and Torsional Pendulum Motion

5 flashcards · 5 quiz questions · 5 match pairs · 3 fill-in sentences · English

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Summary

A simple pendulum is an idealized model that helps explain how many everyday oscillators move. This lesson develops its motion equation and shows why a pendulum can approximate simple harmonic motion.

A simple pendulum consists of a point mass, called the bob, attached to a light string of length $L$ . The string's mass is negligible compared with the bob's mass. The bob moves along an arc, and the forces on it are gravity and tension. Tension acts along the string, so it does not create torque about the pivot. The tangential component of gravity provides the restoring torque.

All flashcards

What is a simple pendulum?: An idealized point-mass bob suspended from a string of negligible mass and length $L$ .
What is a physical pendulum?: A rigid extended object that oscillates about a fixed pivot under gravity.
What is the small-angle period of a physical pendulum?: $T=2\pi\sqrt{I/(mgd)}$ , where $I$ is the moment of inertia about the pivot and $d$ is the pivot-to-center-of-mass distance.
What is a torsion constant?: The measure of a wire's or spring's twisting stiffness in the restoring-torque relation $\tau=-\kappa\theta$ .
What is the small-twist period of a torsional pendulum?: $T=2\pi\sqrt{I/\kappa}$ , where $I$ is rotational inertia about the axis and $\kappa$ is the torsion constant.

Quiz questions

For small oscillations, how does the period of a simple pendulum change if its length is multiplied by four while gravity stays constant?Answer: It doubles, because the period is proportional to the square root of length.
Which expression gives the small-angle period of a physical pendulum?Answer: $T=2\pi\sqrt{I/(mgd)}$
Which expression gives the small-twist period of a torsional pendulum?Answer: $T=2\pi\sqrt{I/\kappa}$
If the rotational inertia stays fixed, what happens to a torsional pendulum's period when its torsion constant increases?Answer: The period decreases, because it is inversely proportional to the square root of the torsion constant.
What idealizations define a simple pendulum?Answer: A point-mass bob is attached to a string whose mass is negligible.

Based on University Physics Volume 1 by William Moebs, Samuel J. Ling, Jeff Sanny (OpenStax), licensed CC BY 4.0. Adapted into a summary, flashcards and quizzes.

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