The change in angular position: $\Delta\theta=\theta_f-\theta_0$.

Angular velocity-time graph slope

The slope of an angular velocity-time graph gives angular acceleration.

Angular acceleration-time graph area

The signed area under an angular acceleration-time graph gives the change in angular velocity.

Radians and revolutions

One revolution corresponds to $2\pi$ radians.

Classical mechanicsLesson 1 of 2 in the course Fixed-Axis Rotation

Constant Angular Acceleration: Equations, Applications, and Graphs

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

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Summary

This lesson introduces the rotational quantities used to describe motion about a fixed axis and explains how constant angular acceleration affects angular velocity.

Angular displacement is measured in radians. The angular velocity $\omega$ describes how quickly angular position changes, while the angular acceleration $\alpha$ describes how quickly angular velocity changes. Their SI units are radians per second ( $\text{rad/s}$ ) and radians per second squared ( $\text{rad/s}^2$ ), respectively.

All flashcards

Angular displacement: The change in angular position: $\Delta\theta=\theta_f-\theta_0$ .
Constant angular acceleration: Angular acceleration that does not change with time; angular velocity then changes linearly with time.
Angular velocity-time graph slope: The slope of an angular velocity-time graph gives angular acceleration.
Angular acceleration-time graph area: The signed area under an angular acceleration-time graph gives the change in angular velocity.
Radians and revolutions: One revolution corresponds to $2\pi$ radians.

Quiz questions

A wheel has initial angular velocity $3\ \text{rad/s}$ and constant angular acceleration $2\ \text{rad/s}^2$ for $4\ \text{s}$ . What is its final angular velocity?Answer: $11\ \text{rad/s}$
Which equation relates final angular velocity, initial angular velocity, angular acceleration, and angular displacement without using time?Answer: $\omega_f^2=\omega_0^2+2\alpha\Delta\theta$
A reel rotates through $220\ \text{rad}$ . Approximately how many revolutions is this?Answer: About $35.0$ revolutions
What physical quantity is represented by the slope of an angular velocity-time graph?Answer: Angular acceleration
What does the signed area under an angular velocity-time graph represent?Answer: Angular displacement

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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