Centripetal Acceleration Calculator

Formula first

Overview

Centripetal acceleration represents the rate of change of the velocity vector's direction for an object moving in a circular path. Even at a constant speed, an object accelerates because its direction is constantly shifting toward the center of rotation.

Symbols

Variables

a = Acceleration, v = Velocity, r = Radius

Apply it well

When To Use

When to use: This equation is used for any object undergoing uniform circular motion or moving along a curved trajectory with a known radius. It assumes the object's path is part of a perfect circle at the moment of measurement.

Why it matters: It is fundamental for calculating the forces needed to keep satellites in orbit, designing safe highway curves, and engineering amusement park rides. Without understanding this acceleration, we could not predict the tension in mechanical rotors or the friction required for vehicles to turn.

Avoid these traps

Common Mistakes

• Using diameter instead of radius.
• Forgetting v is squared.

One free problem

Practice Problem

A race car travels around a circular track with a radius of 50 meters at a constant speed of 20 m/s. Calculate the centripetal acceleration experienced by the car.

Solve for: $a$

Hint: Square the speed first before dividing by the radius.

The full worked solution stays in the interactive walkthrough.

Keep going

Related Formulas

References

Sources

1. Halliday, Resnick, Walker, Fundamentals of Physics
2. Wikipedia: Centripetal acceleration
3. NIST Guide for the Use of the International System of Units (SI) (NIST Special Publication 811, 2008 edition)
4. Fundamentals of Physics, 10th Edition by Halliday, Resnick, and Walker (2014)
5. Halliday, Resnick, and Walker, Fundamentals of Physics
6. Edexcel A-Level Physics — Further Mechanics