Conservation of angular momentum

Conservation of angular momentum is the principle that a system’s total angular momentum remains constant when its net external torque is zero.

Angular momentum: A measure of rotational motion, determined by a system’s mass distribution and motion about an axis. The conserved quantity whose value remains fixed when net external torque vanishes.
Figure skater: An athlete who performs choreographed movements on ice, including rapid spins. Pulling in the arms reduces rotational inertia and increases spin rate.
Rotational motion: Motion in which an object turns about an axis or follows a curved path around a point. Angular momentum describes rotational motion, whether for a rigid body or a particle.
Cavendish experiment: An 18th-century torsion-balance experiment that measured the gravitational attraction between laboratory masses. Its torsion balance illustrates how measurable torque produces angular acceleration rather than preserving angular momentum.
Torque: A measure of how strongly a force tends to change an object’s rotational motion. Net external torque is the condition that determines whether total angular momentum changes.
Diver: An athlete who enters water after leaping or falling from a platform or springboard. Tucking changes body shape and rotation rate during an airborne dive.
Cross product: A vector operation that produces a vector perpendicular to two input vectors, with magnitude tied to their angle. The angular momentum of a particle is defined by the cross product of position and momentum.
Newton's cannonball: A thought experiment in which a cannonball fired horizontally from a high mountain enters an orbit around Earth. Orbital motion offers a setting where central gravity exerts no torque about Earth’s center.
Moment of inertia: A measure of how an object’s mass is distributed relative to a chosen axis of rotation. Changing mass distribution can change rotation speed while angular momentum stays constant.
Gyroscope: A rotating body or device whose angular momentum contributes to its resistance to changes in orientation. Its stability and precession follow from angular momentum’s response to torque.

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