Moment of Inertia: Point Mass

I = m r^{2}

I =

m =

r =

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The building block of all rotational inertia: a compact mass at radius r contributes mr². The square matters — moving mass twice as far from the axis makes it four times harder to spin. Every extended body's moment of inertia is just this formula summed (integrated) over all its mass, which is where the ½ of a disk and the 2/5 of a sphere come from.

Moment of Inertia: Point Mass

I = 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.