Angular Momentum

A measure of an object's rotational “oomph”; for a rigid body spinning about an axis, it equals moment of inertia times angular velocity.

Angular momentum is the rotational counterpart of linear momentum, p = mv. For a point mass, angular momentum about some point is L = r × p, where r is the position vector from that point to the mass and × is the cross product; for a rigid body spinning about a fixed axis, L = Iω, where I is the moment of inertia and ω is angular velocity, measured in kg·m²/s. Its rate of change equals the external torque, dL/dt = τ; with no external torque, angular momentum is conserved — this is why a figure skater spins faster after pulling their arms in. Legged and humanoid robots often track whole-body angular momentum about the center of mass: while airborne, gravity produces no torque about the center of mass, so this quantity stays constant, and the robot can only redistribute it among body parts by swinging its arms or tucking its legs; once a foot touches down, contact forces can change it. Planning for balance, jumping, and flips all has to account for it.

ExampleFor a humanoid robot doing a backflip: it must build up enough angular momentum about its center of mass before its feet leave the ground. Once airborne, total angular momentum stays fixed, so tucking the legs shrinks the moment of inertia to spin faster, and extending them again before landing slows the rotation back down.

Also called

Moment of Momentum

Related

Moment of Inertia · Centroidal Dynamics · Centroidal Momentum Matrix · Torque · Rigid-Body Dynamics · Balance Control

Sources

Angular momentum - Wikipedia