We start by constructing, in our minds, an idealized object for which the mass is all concentrated at a single location which is not on the axis of rotation: Imagine a massless disk rotating about an axis through the center of the disk and perpendicular to its faces. First is a second explanation of inertia. The equations for each of the objects are listed in a table below. Notice for Ixx and Izz that the height and radius of the cylinder affect the inertia, whereas for Iyy, only the radius is considered. ‘I xx‘ can be read as ‘the inertia if rotating about the x-axis’. The result is different for each axis, as shown in the following figure. Notice how the r changees direction from x to y but looks the same between x and z.Įquations have been developed for common shapes so that you don’t have to integrate every time you want to find the inertia of an object. The red r’s in this image show the distance that is being measured when adding up each little infinitesimal dm. Due to the symmetry, rotation about the x axis and z axis looks identical. In this image, rotation about the y axis and x axis produce different types of rotation. You can imagine sticking your pencil into an object and twisting along that axis. As shown in the following figure, rotating about the different axes will produce different types of rotation. A skill that you can develop is your visualization of the rotation about each axis. If there is more mass closer to the axis of rotation, the inertia is smaller. Inertia is always positive and has units of kgm 2 or slugft 2.įor an infinitesimal unit of mass, the inertia depends on how far it is from the axis of rotation.Īs shown in this image, each little dm at r distance from the axis of rotation (y) is added up (through integration). The bigger the inertia, the slower the rotation. Mass moment of inertia, or inertia as it will be referred to from here on, is resistance to rotation. 7.4 Mass Moment of Inertia 7.4.1 Intro to Mass Moment of Inertia
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