By Zencalcy Editorial TeamLast reviewed About us
A rolling object carries energy in two forms: its forward motion and its spin. The split depends on the shape, because shape sets the moment of inertia. A hoop puts more energy into rotation than a solid sphere of the same mass and speed.
Total energy of a rolling hoop, cylinder or sphere.
Hoop: E = m v² Solid cylinder: E = ¾ m v² Solid sphere: E = 0.7 m v²
These follow from E = ½mv² + ½Iω² with ω = v/r and the shape's moment of inertia: mr² for a hoop, ½mr² for a cylinder and ⅖mr² for a solid sphere.
| Symbol | Meaning |
|---|---|
| E | Total kinetic energy, in joules. |
| m | Mass, in kilograms. |
| v | Centre-of-mass speed, in m/s. |
A rolling hoop has 18 J, a solid cylinder 13.5 J and a solid sphere 12.6 J. All three have the same translational 9 J, so the differences come entirely from rotation.
Continue with the Rolling Motion Calculator, Rotational Kinetic Energy Calculator, or the Rotational Kinematics Calculator — or browse more rotational and periodic motion tools and all physics calculators.
Rolling without slipping forces the spin rate to match the speed. A shape with more inertia relative to its mass, like a hoop, spins up more energy for the same forward speed.
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