Uniform Circular Motion & Centripetal Force
1 · Predict
A ball on a rod orbits a fixed central pivot at constant speed. If you increase the ball's orbital speed while keeping the radius the same, does the time for one full lap (the period) get longer, shorter, or stay the same?
- The period gets longer (it takes more time per lap).
- The period stays the same (speed doesn't affect the period).
- The period gets shorter (it takes less time per lap).
2 · Set Up
- Open the Circular Motion preset. Note the rod's length (the orbit radius) and the ball's mass, and confirm gravity is off — the rod alone supplies the force that curves the path.
- Confirm the speed probe is attached to the ball, and drop a Timer on the ball so you can time one full revolution.
- For each trial below, set the ball's mass, the rod length (radius), and its initial tangential speed, then press Play and time one complete lap.
3 · Collect Data
| Mass m (kg) | Radius r (m) | Orbital speed v (m/s) | Centripetal force F = mv²/r (N) | Period T (1 lap) (s) |
|---|---|---|---|---|
| 1 | 2 | 3 | ||
| 1 | 3 | 4 | ||
| 2 | 2.5 | 5 |
Graph the period T (y-axis) against r/v (x-axis) for your three trials. Describe the shape of the line.
4 · Analyze
- For one trial, show your work computing the period from the radius and speed you set (T = 2πr/v) and compare it to the Timer's reading in the sim.
- Across your three trials, how does increasing the speed at a fixed radius change the period? How does increasing the radius at a fixed speed change the period? Explain both using T = 2πr/v.
5 · Extend
- This preset turns gravity off so the motion is genuinely uniform. If gravity were switched back on and the rod still traced a horizontal circle, would the ball's speed stay constant through the whole lap? Why or why not?
- A real orbiting object (like a ball on a string swung by hand) loses a little energy to air resistance and to the pivot each lap. Would you expect its measured period to stay perfectly constant over many laps, or to drift — and in which direction?
The Physics Behind This Experiment
Centripetal Force
The inward force the rod must supply to keep the ball moving in a circle instead of a straight line. It depends on the ball's mass, its (constant) orbital speed, and the radius of the circle — this is the tension you'd feel in the rod at each trial's settings.