Angular Acceleration
Simple Explanation
Angular acceleration (Ξ±) measures how quickly angular velocity itself is changing β how fast a rotation is speeding up or slowing down, in radians per second squared.
Why Do We Need It?
Real rotations rarely spin at a perfectly constant rate β motors spin up, brakes slow wheels down β and angular acceleration is what quantifies exactly how fast that speeding-up or slowing-down happens.
Formula
Angular Acceleration
Ξ± = ΞΟ / Ξt
The rate at which angular velocity changes over time β how quickly a rotation speeds up or slows down.
- Ξ±
- β angular acceleration, in radians per second squared (rad/sΒ²)
- ΞΟ
- β change in angular velocity, in radians per second (rad/s)
- Ξt
- β time interval, in seconds (s)
When to use it: Whenever a rotation is speeding up or slowing down, and the rate of that change is needed.
Worked Example
Find an angular acceleration
A wheel's angular velocity increases from 2 rad/s to 10 rad/s over 4 s. Find its angular acceleration.
Why Does This Work?
This is exactly the rotational analogue of ordinary acceleration β just as acceleration is the rate of change of velocity, angular acceleration is the rate of change of angular velocity.
Real-Life Example
A washing machine drum spinning up
At the start of a spin cycle, a washing machine drum accelerates from rest up to its full spinning speed over a few seconds.
The rate at which the drum's angular velocity increases during that startup is exactly its angular acceleration.
Practice
A wheel's angular velocity increases from 3 rad/s to 15 rad/s over 4 s. Find its angular acceleration.
MediumCommon mistake
Dropping the sign β a rotation that is slowing down has a NEGATIVE angular acceleration (opposite in sign to its angular velocity), not zero.
Quick Review
- Ξ± = ΞΟ/Ξt, in radians per second squared.
- Describes how quickly a rotation speeds up or slows down.
- Negative Ξ± means the rotation is decelerating.