Physics overview
What is angular acceleration?
Angular acceleration describes how quickly angular velocity changes with time. It is used when rotating objects speed up, slow down, or change their rotational rate.
Formula
Angular acceleration formula
Angular Accelerationα = Δω ÷ t
- α is angular acceleration in radians per second squared.
- Δω is the change in angular velocity in radians per second.
- t is elapsed time in seconds.
Worked example
Angular velocity changes by 12 rad/s in 4 seconds
- Write the formula: α = Δω ÷ t.
- Substitute the values: α = 12 ÷ 4.
- Calculate angular acceleration: α = 3 rad/s².
Rearranged equations
Solve for velocity change or time
Angular velocity change
Δω = αt
Multiply angular acceleration by elapsed time.
Time
t = Δω ÷ α
Divide angular velocity change by angular acceleration.
Units
Standard rotational units
Use radians per second squared for angular acceleration, radians per second for angular velocity change, and seconds for time.
Velocity change
Understanding Δω
Angular velocity change is the difference between final and initial angular velocity. In general, Δω = ωf − ωi.
Real-world applications
Where angular acceleration is used
- Motors starting or slowing down.
- Rotating laboratory equipment.
- Wheels, gears, and flywheels.
- Turbines and generators.
- Rotational-motion experiments.
Calculation limits
Important assumptions
- Angular acceleration, velocity change, and time must be greater than zero.
- Angular velocity change must use radians per second.
- Time must match the same motion interval.
- The formula calculates average angular acceleration.
- Units are not converted automatically.
Related tools
Continue your rotational-motion analysis
Use the Angular Velocity Calculator to calculate angular velocity, displacement, or time.
Use the Circular Velocity Calculator to calculate tangential speed, radius, or period.
Questions and answers
Angular acceleration calculator FAQ
What formula does the angular acceleration calculator use?
It uses α = Δω ÷ t, where angular acceleration equals the change in angular velocity divided by elapsed time.
What is angular acceleration?
Angular acceleration measures how quickly angular velocity changes with time and is commonly expressed in radians per second squared.
How do you calculate angular velocity change?
Multiply angular acceleration by time using Δω = αt.
How do you calculate time from angular acceleration?
Divide angular velocity change by angular acceleration using t = Δω ÷ α.