Moment of inertia

scalar measure of the rotational inertia with respect to a fixed axis of rotation

Moment of inertia (${\displaystyle I}$), also called "angular mass" (kg·m2),[1] is the inertia of a rotating body with respect to its rotation.

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

It is a rotating body's resistance to angular acceleration or deceleration, equal to the product of the mass and the square of its perpendicular distance from the axis of rotation.

Moments of inertia for a few objects

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

References

1. Atkinson, P. (2012). Feedback Control Theory for Engineers. Springer Science & Business Media. p. 50. ISBN 978-1-4684-7453-4. The student is advised to regard moment of inertia as being equivalent to 'angular mass'; equations in rotational mechanics are generally analogous to those in translational mechanics. Wherever an equation occurs in translational mechanics involving mass m, there is an equivalent equation in rotational mechanics involving moment of inertia J. The units of moment of inertia are kilogram metres2 (abbreviation kg m2).