It is an extensive (additive) property: the moment of inertia of a rigid composite system is the sum of the moments of inertia of its component subsystems (all taken about the same axis). This formula is similar to the translational kinetic energy Et mv 2.

It depends on the body's mass distribution and the axis chosen, with larger moments requiring more torque to change the body's rotation. It should not be confused with the second moment of area, which is used in bending calculations. Mass moments of inertia have units of dimension mass x length2. Inertia tensor formula for point masses in rigid assembly Asked 2 years, 4 months ago Modified 3 months ago Viewed 985 times 0 Suppose I have N 1kg point masses in a massless rigid assembly such that the center of mass of the assembly is at the origin and point mass i is at ( x i, y i, z i). Because r is the distance to the axis of rotation from each piece of mass that makes up the object, the moment. Example 2.19.1 Calculate for each the moment of inertia about an axis through the center of the sphere. The mass moment of inertia, usually denoted I, measures the extent to which an object resists rotational acceleration about an axis, and is the rotational analogue to mass. for all the point masses that make up the object. The moment of inertia, otherwise known as the angular mass or rotational inertia, of a rigid body is a tensor that determines the torque needed for a desired angular acceleration about a rotational axis. 0(1 kr a), 0(1 kr2 a2), 01 kr2 a2 for the three spheres.

Point mass moment of inertia formula