Moment of Inertia Non Uniform Rod

Moment is the general term used for the tendency of one or more applied forces to rotate an object about an axis but not necessarily to change the angular momentum of the object the concept which is called torque in. The definition of torque states that one or both of the angular velocity or the moment of inertia of an object are changing.

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We would expect the moment of inertia to be smaller about an axis through the center of mass than the endpoint axis just as it was for the barbell example at the start of this section.

. For the derivation of the relations among w V and M consider a simply supported beam subjected to a uniformly distributed load throughout its length as shown in the figure belowLet the shear force and bending moment at a section located at a distance of x from the left support be V and M respectively and at a section x dx be V dV and M dM respectively. Next we calculate the moment of inertia for the same uniform thin rod but with a different axis choice so we can compare the results. Moment of inertia times the angular acceleration or For the first two cases the moment of inertia for a rod rotating about its end is given by Thus for part case a the acceleration is defined only by one torque equal to the force F acting at the full length of the rod L.

Solution

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