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Unformatted text preview: Show that the long diagonal of the cube is a principal axis. (b) If the cube is hanging by a string attached to a corner, and a torque N z is applied about the vertical axis, what will be its angular acceleration? (c) Suppose the body hangs by one of its corners in a uniform gravitational field and swings in a vertical plane. Write down a Lagrangian in terms of the swinging angle and the moment of inertia. What is the frequency of the pendulum? 6. A thin rod of mass m and length l has one end on a table and is balanced vertically. The top of the rod is given a small angular displacement and allowed to fall. (a) Obtain an equation of motion for the angle made by the rod with the table, if the lower end of the rod is not allowed to slide. With what speed does the moving end of the rod hit the table? (b) How does (a) change if it can slide without friction?...
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This note was uploaded on 11/16/2010 for the course PHY 504 taught by Professor Staff during the Fall '08 term at Kentucky.
 Fall '08
 Staff
 mechanics

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