Moment of inertia

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.

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

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.

Related pages

References

↑ 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).

Other websites

Angular momentum and rigid-body rotation in two and three dimensions
A table of moments of inertia Archived 2008-07-01 at the Wayback Machine
Parallels between rotation and translation HyperPhysics

[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).

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