Example 9-4 - I about the y axis, we choose a mass element...

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Moment of Inertia of a Thin Uniform Rod Find the moment of inertia of a thin uniform rod of length  and mass  about an axis  perpendicular to the rod and through one end. PICTURE  Use  ( Equation       9-13     ) to calculate the moment of inertia about the specified axis. The  rod is uniform, which means that for any segment of the rod, the mass per unit length  λ  is equal to  M/L . SOLVE   1. Draw a sketch ( Figure       9-6     ) showing the rod along the + x  axis with its end at the origin. To  calculate 
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Unformatted text preview: I about the y axis, we choose a mass element dm at a distance x from the axis: 2.The moment of inertia about the y axis is given by the integral: Answer: 3. To compute the integral, we first relate dm to dx. Express dm in terms of the linear mass density and dx : Answer: 4. Substitute and perform the integration. We choose integration limits so that we integrate through the mass distribution in the direction of increasing x : Answer:...
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