Constant angular acceleration gives a quadratic change in rotation angle over time.
Difficulty
Intermediate
Read time
5 min
Prerequisites
Basic algebra, consistent units, and the stated model assumptions
Source
OpenStax, College Physics 2e, §10.1 (Paul Peter Urone and Roger Hinrichs)OpenFormulaGraph equation reference; FormuLab adaptation details and license are provided below.
Adapted from OpenFormulaGraph, under CC BY 4.0.
FormuLab adapted wording, notation, applicability conditions and topic placement, and expanded the numerical check into a worked example.
Constant angular acceleration gives a quadratic change in rotation angle over time. The initial angular velocity contributes a term proportional to time, while angular acceleration contributes a term proportional to time squared.
| Symbol | Meaning | Units |
|---|---|---|
| Angular displacement | ||
| Angular Velocity (initial) | ||
| Angular Acceleration | ||
| Time |
Find angular travel during uniform spin-up.
Compare rotation angles for different acceleration intervals.
A rotor starts from rest and maintains angular acceleration 2 rad/s² for 3 s. Find its angular displacement.
OpenFormulaGraph equation reference; FormuLab adaptation details and license are provided below.
Adapted from OpenFormulaGraph, under CC BY 4.0.
FormuLab adapted wording, notation, applicability conditions and topic placement, and expanded the numerical check into a worked example.
Assumptions
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