5.4.A—Describe the rotational inertia of a rigid system relative to a given axis of rotation

Describe the rotational inertia of a rigid system relative to a given axis of rotation.

• Rotational inertia measures a rigid system’s resistance to changes in rotation and is related to the mass of the system and the distribution of that mass relative to the axis of rotation.
• The rotational inertia of an object rotating a perpendicular distance r from an axis is described by the equation Im r2= .
• The total rotational inertia of a collection of objects about an axis is the sum of the rotational inertias of each object about that axis.
• For a solid that can be considered as a collection of differential masses, dm, the solid’s rotational inertia can be calculated using the equation where r is the perpendicular distance from dm to the axis of rotation.