Arc length is proportional to rotation angle and radius.
Difficulty
Intermediate
Read time
5 min
Prerequisites
Basic algebra, consistent units, and the stated model assumptions
Source
OpenStax, College Physics 2e, §6.1 (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.
Arc length is proportional to rotation angle and radius. A full revolution corresponds to an angle of 2π radians.
| Symbol | Meaning | Units |
|---|---|---|
| Arc length swept out | ||
| Radius | ||
| Rotation angle in radians |
Relate angular travel to distance along a circumference.
Find arc motion of a point on a rotating part.
A point moves through 1.5 rad on a circle of radius 2 m. Find the arc length.
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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