# Centripetal Acceleration Calculator

Note
• Enter the values of the two known variables in the text boxes
• Leave the text box empty for the variable you want to solve for
• Click on the calculate button.

Formula used
$a=\frac {v^2}{r}$
Where $a$ -> Centripetal Acceleration
$v$ -> Linear velocity
$r$ -> Radius

### Centripetal Acceleration Calculator

What is Centripetal Acceleration
Centripetal Acceleration is the property of the object moving in circular motion. It is defined as the acceleration vector which is acting towards the center of the cicle at every point on the motion.
Centripetal Acceleration Formula is
$a_c = \frac {v^2}{R}$
Where
$a_c$ is the centripetal Acceleration
$v$ is the velocity of the object
$R$ is the radius of the circle
SI unit of Centripetal Acceleration is same as acceleration i.e m/s2. It is a vector quantity

Example of Few questions where you can use this centripetal Acceleration Calculator
Question 1
Calculate the Centripetal acceleration of the object moving in a circle of radius 10m with velocity 10m/s
Solution
Given, r=10 m.,v=10 m/s, $a_c$=? Centripetal Acceleration is given by
$a_c = \frac {v^2}{R}$
$a_c = \frac {10^2}{10} = 10 / m/s^2$

Question 2
An 0bject is moving on a circular path with velocity 5m/s .Its centripetal acceleration is 2 m/s2. Find the radius of the circular path?
Solution
Given, r=?,v=5 m/s, $a_c=2 \ m/s^2$ Centripetal Acceleration is given by
$a_c = \frac {v^2}{R}$
Rearranging for radius $R= \frac {v^2}{a_c}$
$R= \frac {5^2}{2} = 12.5 \ m$
Question 3
An body is moving on a circular path of Radius 50 m.Its centripetal acceleration is 2 m/s2. Find the velocity of the body
Solution
Given, r=10,v=?, $a_c=2 \ m/s^2$ Centripetal Acceleration is given by
$a_c = \frac {v^2}{R}$
Rearranging for Velocity $v= \sqrt {a_c R}$
$R= \sqrt {2 \times 50 }= 10 \ m/s$

## How Centripetal Acceleration Calculator works

• If velocity and radius is given, Centripetal acceleration is calculated as
$a_c = \frac {v^2}{R}$
• If velocity and Centripetal acceleration is given, Radius is calculated as
$R= \frac {v^2}{a_c}$
• If Radius and Centripetal acceleration is given, velocity is calculated as
$v= \sqrt {a_c R}$