Enter the linear acceleration and the radius to determine the Angular Acceleration. 

Angular Acceleration Formula

The following equation is used to calculate the Angular Acceleration.

A = LA / r
  • Where A is the Angular Acceleration (rad/s^2)
  • LA is the linear acceleration (m/s^2)
  • r is the radius (m)

To calculate the angular acceleration, divide the linear acceleration by the radius.

What are the units for Angular Acceleration?

The most common units for Angular Acceleration are rad/s^2.

How to Calculate Angular Acceleration?

Example Problem:

The following example problem outlines the steps and information required to calculate the Angular Acceleration.

First, determine the linear acceleration. In this example, the linear acceleration is measured to be 40 (m/s^2).

Next, determine the radius. For this problem, the radius is calculated to be 10 (m).

Finally, calculate the Angular Acceleration using the formula above: 

A = LA / r

Inserting the values from above and solving the equation gives us: 

A = 40 / 10 = 4 (rad/s^2)

FAQ

What is the difference between linear and angular acceleration?

Linear acceleration refers to the rate of change of velocity of an object moving along a straight path, measured in m/s^2. Angular acceleration, on the other hand, is the rate of change of angular velocity of an object in rotational motion, measured in rad/s^2. While linear acceleration deals with changes in the speed of an object moving in a straight line, angular acceleration deals with changes in the rotational speed of an object.

Can angular acceleration be negative?

Yes, angular acceleration can be negative. A negative angular acceleration indicates that the angular velocity of the rotating object is decreasing over time, meaning the object is slowing down in its rotational motion. This is also referred to as deceleration in a rotational context.

How is angular acceleration applied in real-life scenarios?

Angular acceleration is applied in various real-life scenarios, including the design and operation of machinery with rotating parts, such as turbines, engines, and wheels. It is also crucial in sports science for analyzing movements in sports like gymnastics, figure skating, and discus throw, where rotational motion plays a key role. Additionally, it is used in the study of celestial bodies and their rotational dynamics in astrophysics.