By Zencalcy Editorial TeamLast reviewed About us
A spinning object stores energy even if its centre stays still. That rotational kinetic energy is ½Iω², the rotational analogue of ½mv², and it is why a flywheel can smooth out an engine's power delivery.
Energy stored in a spinning object.
E_r = ½ I ω²
E_r is rotational kinetic energy in joules, I is the moment of inertia in kg·m² and ω is angular velocity in rad/s. For a rolling object, add the translational energy ½mv².
| Symbol | Meaning |
|---|---|
| E_r | Rotational kinetic energy, in joules. |
| I | Moment of inertia, in kg·m². |
| ω | Angular velocity, in rad/s. |
The energy is ½ × 2 × 10² = 100 J. Doubling the angular velocity to 20 rad/s stores 400 J, four times as much.
Continue with the Rotational Kinematics Calculator, Rotational Power Calculator, or the SHM Acceleration Calculator — or browse more rotational and periodic motion tools and all physics calculators.
Energy is torque integrated over angle. Because torque rises linearly with angle for a constant angular acceleration, the average torque is half the final value, giving the factor of one half.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
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Last reviewed: September 2026. See how we build and check every tool on the about page.
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Content updated: September 2026