About the Circular Motion Calculator
What is the Circular Motion Calculator?
An object moving in a circle constantly changes direction, which needs an inward centripetal force. For a car on a curve it comes from tyre friction; for a satellite, from gravity.
Enter mass, radius and speed to get the force, the acceleration in m/s² and in g, and the time for one revolution.
How to use the Circular Motion Calculator
- Mass (kg) (sample: 1)
- Radius (m) (sample: 2)
- Speed (m/s) (sample: 4)
- Press Calculate Circular Motion (results also refresh as you type). The result card shows the Centripetal Force, along with Centripetal acceleration, In g, Angular velocity and Period of one revolution.
Formula used
F = m × v² ÷ r
- a = v² ÷ r
- ω = v ÷ r (rad/s)
- Period = 2π ÷ ω
Doubling speed on the same curve needs four times the force.
Worked example
These are the sample values already filled in the calculator above, and the result it returns for them:
| Input | Sample value |
|---|---|
| Mass (kg) | 1 |
| Radius (m) | 2 |
| Speed (m/s) | 4 |
| Result | Value |
|---|---|
| Centripetal Force | 8 N |
| Centripetal acceleration | 8 m/s² |
| In g | 0.816 g |
| Angular velocity | 2 rad/s |
| Period of one revolution | 3.142 s |
| Revolutions per minute | 19.1 rpm |
Tips for using the Circular Motion Calculator
- On wet roads, lower friction limits the centripetal force – slow down on curves.
- Banked roads and tracks let part of the normal force provide the centripetal force.