Angular acceleration is the rotational counterpart of linear acceleration. Spinning up a hard drive, a car wheel accelerating or a figure skater changing speed all involve angular acceleration, measured in rad/s².
How to use the Angular Acceleration Calculator
- Method
- Initial angular velocity ω₀
- Final angular velocity ω₁
- Time t
- Torque τ
- Moment of inertia I
- Tangential acceleration a_t
- Radius r
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose the method. Angular velocities can be entered in rad/s, rpm or revolutions per second.
Inputs explained
| Field | What to enter |
|---|---|
| Method | Choose one: Angular velocity difference, Torque and moment of inertia, Tangential acceleration and radius |
| Initial angular velocity ω₀ | Units: rad/s, rpm, Hz (rev/s), °/s |
| Final angular velocity ω₁ | Units: rpm, rad/s, Hz (rev/s) |
| Time t | Units: s, ms, min, h, days |
| Torque τ | Units: N·m, kN·m, lbf·ft, lbf·in, kgf·m |
| Moment of inertia I | Units: kg·m², g·cm², lb·ft², lb·in² |
| Tangential acceleration a_t | Units: m/s², ft/s², g, cm/s² |
| Radius r | Units: m, cm, mm, km, in, ft … |
Formula
α = (ω₁ − ω₀)/t · α = τ/I · α = a_t / r
Worked example
Inputs — Method: Angular velocity difference; Initial angular velocity ω₀: 0 rad/s; Final angular velocity ω₁: 3,000 rpm; Time t: 5 s.
Results — Angular acceleration α = 62.8319 rad/s².
Key terms
- Angular acceleration
- Rate of change of angular velocity.
Frequently asked questions
What is the unit of angular acceleration?
Radians per second squared (rad/s²).
How is it related to linear acceleration?
a_t = α·r at radius r.
What is the rotational version of F = ma?
τ = I·α.
Can angular acceleration be negative?
Yes – when the rotation slows down.