Definition

Angular momentum

L = r \times p = I ω

Statement

For a particle, the cross product of position and momentum; for a rigid body, moment of inertia times angular velocity.

Symbols and units

$L$	angular momentum	kg·m²/s
$I, ω$	moment of inertia, angular velocity	kg·m², rad/s
$r$	position from axis to particle	m
$p$	linear momentum	kg·m/s

When it applies

Any particle or rigid body, about a specified point or axis.

Derivation

Defined by direct analogy with linear momentum, using the cross product to capture rotation about a point:

L = r \times p

For a rigid body rotating about a fixed axis, this reduces to:

L = I ω

Worked examples

Angular momentum of a spinning disk

I = 0.50 kg·m², ω = 6.0 rad/s:

L = I ω = (0.50) (6.0) = 3.0 kg\cdotm^{2} /s

Watch out for

Like torque, angular momentum depends on the choice of reference point or axis — always state which one is being used.

Connects to