Angular Acceleration Calculator

What Is Angular Acceleration?

Angular acceleration is the rate at which an object's angular velocity changes over time. It is the rotational equivalent of linear acceleration. Angular acceleration is measured in radians per second squared (rad/s²).

When a motor spins up from rest, or a spinning wheel slows to a stop, angular acceleration describes how quickly that rotational speed changes. A positive angular acceleration means the object is spinning faster, while a negative value means it is slowing down.

How to Calculate Angular Acceleration

To calculate angular acceleration, you need the initial angular velocity, the final angular velocity, and the time interval over which the change occurs.

Angular Acceleration Formula

The formula to find angular acceleration is:

Where:

• α = angular acceleration (rad/s²)
• ω₁ = initial angular velocity (rad/s)
• ω₂ = final angular velocity (rad/s)
• t = time (s)

For example, let's find the angular acceleration of a motor that spins up from rest to 1,800 RPM in 5 seconds. First, convert RPM to rad/s: 1,800 × 2π / 60 = 188.5 rad/s.

α = (188.5 − 0) / 5 = 37.7 rad/s²

Relationship to Linear Acceleration

Angular acceleration and linear acceleration are connected through the radius: a = α × r. A point on the rim of a spinning wheel at radius r experiences a tangential (linear) acceleration proportional to α. This relationship is important for calculating centripetal force and centrifugal force in rotating systems.