A spinning object stores kinetic energy even if its centre does not move. Flywheels, turbines, wheels and planets all hold rotational kinetic energy; a rolling ball has both rotational and translational energy.
How to use the Rotational Kinetic Energy Calculator
- Angular velocity ω
- Moment of inertia I
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the moment of inertia and the angular velocity (rad/s, rpm or Hz).
Inputs explained
| Field | What to enter |
|---|---|
| Angular velocity ω | Units: rpm, rad/s, Hz (rev/s) |
| Moment of inertia I | Units: kg·m², g·cm², lb·ft², lb·in² |
What each result means
- Rotational kinetic energy = [Moment of inertia I]×[Angular velocity ω]^2÷2
- Angular momentum = [Moment of inertia I]×[Angular velocity ω]
Example values
How the main result changes when Angular velocity ω changes and everything else stays at the example values above:
| Angular velocity ω (rpm) | Rotational kinetic energy (J) |
|---|---|
| 1,500 | 616.8503 |
| 2,250 | 1,387.9131 |
| 3,000 | 2,467.4011 |
| 3,750 | 3,855.3142 |
| 4,500 | 5,551.6525 |
| 6,000 | 9,869.6044 |
Formula
E = ½·I·ω²
Worked example
Inputs — Angular velocity ω: 3,000 rpm; Moment of inertia I: 0.05 kg·m².
Results — Rotational kinetic energy = 2,467.4011 J; Angular momentum = 15.70796 kg·m²/s.
Key terms
- Rotational kinetic energy
- ½Iω².
Frequently asked questions
How does speed affect rotational energy?
It grows with ω² – double the rpm, four times the energy.
What is the total energy of a rolling ball?
½mv² + ½Iω².
Where is rotational energy stored usefully?
Flywheels and turbines.
What are the units?
Joules.