Moment of inertia

The angular momentum of the figure skater is conserved—as she decreases her radius by retracting her arms and legs, her moment of inertia decreases, but her angular velocity increases to compensate.

Moment of inertia ([math]\displaystyle{ I }[/math]), also called "angular mass" (kg·m²),^[1] is a body's resistance to angular acceleration or deceleration, equal to the product of the mass and the square of its radius measured perpendicularly to the axis of rotation.

Moments of inertia for a few objects

The moment of inertia I = ∫r²dm of a hoop, disk, cylinder, box, plate, rod, and spherical shell or solid can be found from this figure.

Moment Of Inertia Media

Tightrope walkers use the moment of inertia of a long rod for balance as they walk the rope. Samuel Dixon crossing the Niagara River in 1890.
Video of rotating chair experiment, illustrating moment of inertia. When the spinning professor pulls his arms, his moment of inertia decreases; to conserve angular momentum, his angular velocity increases.
Pendulums used in Mendenhall gravimeter apparatus, from 1897 scientific journal. The portable gravimeter developed in 1890 by Thomas C. Mendenhall provided the most accurate relative measurements of the local gravitational field of the Earth.
Rolling Racers - Moment of inertia
Moment of inertia rod center
Moment of inertia solid sphere
The cylinders with higher moment of inertia roll down a slope with a smaller acceleration, as more of their potential energy needs to be converted into the rotational kinetic energy.
This 1906 rotary shear uses the moment of inertia of two flywheels to store kinetic energy which when released is used to cut metal stock (International Library of Technology, 1906).
A 1920s John Deere tractor with the spoked flywheel on the engine. The large moment of inertia of the flywheel smooths the operation of the tractor.