Moment of inertia

"the rotational equivalent of mass in its mechanical effect, that is, the resistance to a change of state (a speeding up or slowing down) during rotation" (Rodgers & Cavanagh, 1984).

A mass' moment of inertia depends on how that mass is distributed about an axis of rotation.

For example, the leg's distal mass, which moves about the knee's lateral axis (designated by the x in the diagram to the left), possesses moment of inertia with respect to that axis.

estimating moment of inertia

We can calculate the lower leg's moment of inertia by measuring

  • the mass of each of i parts and

  • the distances ri at which those parts lie from the axis of rotation.


I= m1r12 + m2r22 + m3r32 + ... + mnrn2

The more parts into which we divide the mass, the more accurate our estimate of its moment of inertia.

Anthropometric tables often include estimates of body segment moment of inertia. Researchers use these, rather than direct measurements, to perform biomechanical analyses.


Rodgers, M.M., & Cavanagh, P.R. (1984). Glossary of Biomechanical terms, concepts, and units. Physical Therapy, 64, 1886-1902.

Last updated 4-19-01 © Dave Thompson PT