Centripetal Acceleration Formula
Calculate the acceleration of an object moving in a circle using a = v²/r.
Includes examples and real-world applications.
The Formula
Centripetal acceleration is the rate of change of velocity direction for an object moving along a curved path. It always points toward the center of the circle.
Even if the speed stays constant, the direction changes continuously. That change in direction IS acceleration — centripetal acceleration.
Variables
| Symbol | Meaning |
|---|---|
| a | Centripetal acceleration (m/s²) |
| v | Linear velocity / speed of the object (m/s) |
| r | Radius of the circular path (meters) |
Alternative Form (using angular velocity)
Where ω (omega) is the angular velocity in radians per second. The two forms are equivalent because v = ωr.
Example 1
A car drives around a roundabout (radius 25 m) at 10 m/s
a = 10² / 25
a = 100 / 25
a = 4 m/s² (about 0.4 g)
Example 2
A satellite orbits Earth at 7,800 m/s at an altitude of 400 km (r = 6,771,000 m from Earth's center)
a = 7800² / 6,771,000
a = 60,840,000 / 6,771,000
a = 8.99 m/s² (nearly equal to g at that altitude)
Example 3
A cyclist rounds a curve (radius 10 m) at 6 m/s
a = 6² / 10
a = 36 / 10
a = 3.6 m/s²
When to Use It
- Determining how much grip a car needs on a curved road
- Calculating g-forces on roller coasters and in airplane turns
- Designing centrifuges for laboratory or industrial use
- Analyzing orbital mechanics for satellites and planets
- Understanding why objects feel heavier on spinning amusement rides
Key Relationships
- Doubling the speed quadruples the centripetal acceleration (because v is squared)
- Halving the radius doubles the acceleration
- Centripetal acceleration multiplied by mass gives centripetal force: F = ma = mv²/r