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рн FIND MOMENT OF INERTIA OF A RIGID BODYThe moment of inertia of a symmetrical body rotating about its axis of symmetry can be found by finding the moment of inertia of a small element of it about the axis of rotation and then integrating it within the proper limits for whole of the body. Consider that a small elementary portion of mass The moment of inertia of the whole rigid body about the axis of rotation,
If the rigid body is made of material of uniform density
In using this equation, we express the volume element dV in terms of the differentials of the integration variables, usually the coordinates of the volume elements. The element dV must always be chosen so that all points within it are at very nearly the same distance from the axis of rotation. For regularly shaped bodies this integration can be after be carried out quite easily. Discuss several examples. In case the rigid body is a plane lamina, where dA is area of the elementary portion of the plane lamine and 5.3.1. Uniform slender rod; axis perpendicular to length rod Rod has mass
The ratio of the mass Where Using (70) we obtain:
From this general expression we can find the moment of inertia about an axis through any point of the rod. For example, if the axis is at the left end, If the axis is the right end As would be expected, if the axis passes though the center, Date: 2015-01-12; view: 1896
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