About the Angular Acceleration Calculator
This calculator finds angular acceleration — how quickly an object's rotational speed changes — from its initial and final angular velocity and the time it took to change. It also converts that result into the tangential (linear) acceleration felt by a point at a given radius from the axis of rotation.
The formulas
- Angular acceleration: α = (ω − ω₀) / Δt, where ω₀ and ω are the initial and final angular velocities in radians per second (rad/s) and Δt is the elapsed time in seconds. The result is in radians per second squared (rad/s²).
- Tangential acceleration: a = α × r, where r is the distance from the axis of rotation in meters. This is the linear acceleration of a point on the rotating object, in m/s².
- Unit conversion: multiply rad/s² by 180/π (≈57.2958) to get deg/s², or by 60/(2π) (≈9.5493) to get RPM per second.
Getting accurate results
- Angular velocity must be entered in radians per second. If you have a value in RPM, multiply by 2π/60 (≈0.10472) first to convert.
- Pick a consistent positive rotation direction before entering values; a negative ω or α simply means motion opposite to that chosen direction.
- This formula gives the average angular acceleration over the interval. If the true acceleration is not constant, it will differ from the instantaneous value at any single moment within Δt.
Frequently Asked Questions
What is the formula for angular acceleration?
Angular acceleration (α) equals the change in angular velocity divided by the time it took: α = (ω − ω₀) / Δt. With angular velocities in radians per second and time in seconds, the result is in radians per second squared (rad/s²).
How do I convert angular acceleration to tangential acceleration?
Multiply the angular acceleration by the radius (the distance from the axis of rotation): a = α × r. If α is in rad/s² and r is in meters, the tangential acceleration a comes out in m/s².
What does a negative angular acceleration mean?
Once you pick a positive rotation direction, a negative α means the angular velocity is changing in the opposite direction from that choice. Depending on the signs of ω₀ and ω, that can mean the object is slowing down, speeding up while spinning the other way, or reversing direction.
How do I convert rad/s² to deg/s² or RPM per second?
Multiply rad/s² by 180/π (about 57.2958) to get deg/s². To get RPM per second, multiply rad/s² by 60/(2π) (about 9.5493).