Centripetal Acceleration Calculator

Understanding Centripetal Acceleration Calculator

Centripetal acceleration always points toward the center of the circular path. It is responsible for changing the direction of velocity.

How to use this calculator

1. Enter the object speed, usually in meters per second, as the value of \(v\).
2. Enter the radius of the circular path, in meters, as the value of \(r\).
3. Check that both values use compatible units, because the result will be in meters per second squared.
4. Read the calculated centripetal acceleration, \(a_c\), from the result.

The formula explained

The formula \(a_c = \frac{v^2}{r}\) computes the centripetal acceleration for an object moving in a circle. It shows that faster speed increases acceleration, while a larger radius decreases it.

• \(a_c\) = centripetal acceleration, in \(\mathrm{m/s^2}\)
• v = speed of the object, in \(\mathrm{m/s}\)
• r = radius of the circular path, in \(\mathrm{m}\)

Step by step method

1. Square the speed, so compute \(v^2\).
2. Divide \(v^2\) by the radius \(r\).
3. Write the answer with units of \(\mathrm{m/s^2}\).

Worked example

Problem. A car moves at \(12\,\mathrm{m/s}\) around a curve with radius \(18\,\mathrm{m}\). Find the centripetal acceleration.

1. Use \(a_c = \frac{v^2}{r}\).
2. Substitute the values, \(a_c = \frac{12^2}{18} = \frac{144}{18}\).
3. Compute the result, \(a_c = 8\,\mathrm{m/s^2}\).

Tips and common mistakes

• Make sure the radius is the distance from the center of the circle to the object, not the full diameter.
• If you double the speed, the centripetal acceleration becomes four times larger, because the speed is squared.

Frequently asked questions