Indeed, the rotational inertia of an object. Rotational inertia plays a similar role in rotational mechanics to mass in linear mechanics. It is a scalar value which tells us how difficult it is to change the rotational velocity of the object around a given rotational axis. Two point masses, m 1 and m 2, with reduced mass μ and separated by a distance x, about an axis passing through the center of mass of the system and perpendicular to the line joining the two particles. Rotational inertia is a property of any object which can be rotated. Point mass M at a distance r from the axis of rotation.Ī point mass does not have a moment of inertia around its own axis, but using the parallel axis theorem a moment of inertia around a distant axis of rotation is achieved.

In general, the moment of inertia is a tensor, see below. This article mainly considers symmetric mass distributions, with constant density throughout the object, and the axis of rotation is taken to be through the center of mass unless otherwise specified.įollowing are scalar moments of inertia. When calculating moments of inertia, it is useful to remember that it is an additive function and exploit the parallel axis and perpendicular axis theorems. In general, it may not be straightforward to symbolically express the moment of inertia of shapes with more complicated mass distributions and lacking symmetry. Typically this occurs when the mass density is constant, but in some cases the density can vary throughout the object as well. The mass moment of inertia is often also known as the rotational inertia, and sometimes as the angular mass.įor simple objects with geometric symmetry, one can often determine the moment of inertia in an exact closed-form expression.

It should not be confused with the second moment of area, which has units of dimension L 4 ( 4) and is used in beam calculations. The moments of inertia of a mass have units of dimension ML 2 ( × 2). Moment of inertia, denoted by I, measures the extent to which an object resists rotational acceleration about a particular axis, it is the rotational analogue to mass (which determines an object's resistance to linear acceleration).

Moment of inertia equation