Centripetal Acceleration Calculator

Calculate the centripetal acceleration based on tangential velocity and radius or angular velocity.

Input Parameters

Calculation Results

Calculation Formula

Centripetal Acceleration (a) = v²/r = ω²r

Where:
a = centripetal acceleration (m/s²)
v = tangential velocity (m/s)
r = radius (m)
ω = angular velocity (rad/s)

Result

Centripetal Acceleration Calculator Usage Guide

Learn how to use the Centripetal Acceleration Calculator and its working principles

How to Use

  1. Enter the tangential velocity (v) in meters per second (m/s)
  2. Enter the radius (r) in meters (m)
  3. Alternatively, enter the angular velocity (ω) in radians per second (rad/s)
  4. Click the "Calculate" button to compute the centripetal acceleration
  5. The result will be displayed in meters per second squared (m/s²)

Principle Explanation

Centripetal acceleration is the acceleration that causes an object to follow a curved path and is always directed toward the center of the curve. For an object moving in a circle of radius r with a constant speed v, the centripetal acceleration is given by:

a = v²/r = ω²r

Where:

  • a = centripetal acceleration (m/s²)
  • v = tangential velocity (m/s)
  • r = radius (m)
  • ω = angular velocity (rad/s)

Example

If a car is moving at a speed of 20 m/s around a circular track with a radius of 100 meters, what is the centripetal acceleration?

Using the formula: a = v²/r = (20)²/100 = 400/100 = 4 m/s²