If the thickness is not negligible, then the expression for I of a cylinder about its end can be used.Ĭalculating the moment of inertia of a rod about its center of mass is a good example of the need for calculus to deal with the properties of continuous mass distributions. ![]() The moment of inertia about the end of the rod is The moment of inertia about the end of the rod can be calculated directly or obtained from the center of mass expression by use of the Parallel axis theorem. HyperPhysics***** Mechanics ***** Rotationįor a uniform rod with negligible thickness, the moment of inertia about its center of mass is This process leads to the expression for the moment of inertia of a point mass. This provides a setting for comparing linear and rotational quantities for the same system. ![]() If the mass is released from a horizontal orientation, it can be described either in terms of force and accleration with Newton's second law for linear motion, or as a pure rotation about the axis with Newton's second law for rotation. Moment of Inertia Rotational and Linear ExampleĪ mass m is placed on a rod of length r and negligible mass, and constrained to rotate about a fixed axis.
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