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Angular Displacement Visualization

Run the Angular Displacement MicroSim Fullscreen

About This MicroSim

This simulation teaches one concept clearly: arc length depends on radius (s = rθ). Two colored points at different radii rotate through the same angle, making it visually obvious that the outer point travels a longer arc.

How to Use

  1. Drag the slider to change the angular displacement θ
  2. Observe how both points rotate through the same angle
  3. Compare the arc lengths (shown as thick colored arcs)
  4. Check the ratio in the info panel - it equals the ratio of the radii

Key Insight

Both points always rotate through the same angle θ, but the outer point (green, r=180) travels 3 times farther than the inner point (red, r=60) because arc length is proportional to radius:

s = r × θ

Iframe Embed Code

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<iframe src="https://dmccreary.github.io/intro-to-physics-course/sims/angular-displacement/main.html"
        height="552px"
        width="100%"
        scrolling="no">
</iframe>

Discussion Questions

  1. If you double the radius, what happens to the arc length for the same angle?
  2. Why must we use radians (not degrees) in the s = rθ formula?
  3. How does this explain why the outer edge of a merry-go-round moves faster than the center?