Moment of Inertia: Solid Disk

I = \tfrac{1}{2} m r^{2}

I =

m =

r =

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A solid disk's mass is spread from the axis out to the rim, and the integration averages that spread to exactly half of mr². Compare the extremes: a hoop with all mass at the rim has I = mr² and a solid disk of the same mass and radius has half that — which is why the disk wins a rolling race down an incline. Flywheels, grinding wheels, and hard-disk platters all compute their stored energy from this ½mr².

Moment of Inertia: Solid Disk

I = \tfrac{1}{2} m r^{2}

Where

$I$ = Moment of inertia
$m$ = Mass
$r$ = Radius

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

Moment of inertia — Newton's Second Law for Rotation (τ = Iα), Rotational Kinetic Energy
Mass — Newton's Second Law, Kinetic Energy
Radius — Centripetal Acceleration (a = v²/r), Centripetal Force (F = mv²/r)

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.