Rotational Kinetic Energy

KE_{rot} = \tfrac{1}{2} I \omega^{2}

KE =

I =

ω =

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Substitute I for m and ω for v in ½mv² and you have the energy of anything that spins. It is real, usable energy: grid-scale flywheel batteries store megajoules by spinning steel or carbon-fiber rotors at tens of thousands of rpm, and a rolling wheel carries both translational ½mv² and rotational ½Iω² — the reason a solid cylinder beats a hollow hoop down a ramp.

Rotational Kinetic Energy

KE_{rot} = \tfrac{1}{2} I \omega^{2}

Where

$KE_{rot}$ = Rotational kinetic energy
$I$ = Moment of inertia
$\omega$ = Angular velocity

Missing one of these? Work it out first, then come back

Rotational kinetic energy — Kinetic Energy, Power (P = W/t)
Moment of inertia — Newton's Second Law for Rotation (τ = Iα), Angular Momentum (L = Iω)
Angular velocity — Angular Velocity (ω = θ/t), Angular Velocity from Period

Part of this formula set

The rotational equations of motion

13 formulasThe angular twins of the linear equations — θ, ω and α in place of d, v and a, and torque, moment of inertia and Iω in place of F, m and p.