Centripetal Force Formula
Calculate the force needed to keep an object moving in a circle.
Applies to cars on curves, satellites, and spinning objects.
The Formula
F = mv² / r
Centripetal force is the inward force required to keep an object moving in a circular path. Without this force, the object would fly off in a straight line (Newton's first law).
Variables
| Symbol | Meaning |
|---|---|
| F | Centripetal force (Newtons) |
| m | Mass of the object (kg) |
| v | Velocity of the object (m/s) |
| r | Radius of the circular path (meters) |
Example 1
A 1,200 kg car goes around a curve (radius 50 m) at 15 m/s
F = 1200 × 15² / 50
F = 1200 × 225 / 50
F = 5,400 N (provided by tire friction)
Example 2
A 0.5 kg ball on a 1 m string swings at 4 m/s
F = 0.5 × 4² / 1
F = 0.5 × 16
F = 8 N (tension in the string)
When to Use It
Use the centripetal force formula when:
- Designing road curves and banked turns
- Calculating the tension in a string for circular motion
- Understanding roller coaster forces at loops
- Analyzing satellite orbits and centrifuge systems