Mass moment

Moment of inertia unit mm4

Mass moment of inertia, or inertia as it will be referred to from here on, is resistance to rotation. The bigger the inertia, the slower the rotation. Inertia is always positive and has units of kgm 2 or slugft 2. For an infinitesimal unit of mass, the inertia depends on how far it is from the axis of rotation. As shown in this image, each little dm at r distance from the axis of rotation y is added up through integration.

If r is bigger, the inertia is bigger. If there is more mass closer to the axis of rotation, the inertia is smaller. A skill that you can develop is your visualization of the rotation about each axis. As shown in the following figure, rotating about the different axes will produce different types of rotation. You can imagine sticking your pencil into an object and twisting along that axis.

In this image, rotation about the y axis and x axis produce different types of rotation. Due to the symmetry, rotation about the x axis and z axis looks identical.