HW6 - together to form a rigid body a What is the inertia...

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Physics 110, Problem set #6 Due on May 26, 2010 1. Inertia tensor (25 points): Find the inertia tensors for the following rigid bodies. Set the center of mass to be the origin of coordinates. Choose the orientation of the coordinate system wisely so that the axes coincide with the principal axes. You need to justify your selections by showing that the off-diagonal terms vanish. a. Four point masses (mass= m for 3, and m 2 for the 4 th ) connected by massless rods (length= l for each one) to form an equilateral tetrahedron. (7 pts) b. A plank, with dimensions h w l , , and mass M . (7 pts) c. A thin disk, with radius r and mass M . (5 pts) d. A cylinder with radius r , height h , and mass M (6 pts). 2. Inertia tensor (40 pts): 3 unit point masses: (0,0,0), (4,0,0), (0,3,0) are joined
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Unformatted text preview: together to form a rigid body. a. What is the inertia tensor with respect to the origin? (7 pts) b. Find the inertia tensor with respect to the center of mass (C.M.). (6 pts) c. Find the principal moments with respect to the C.M. (6 pts) d. Find the principal axes with respect to the C.M. (6 pts) e. What is the direction and magnitude of the torque that is required to spin the system (around its C.M.) at a constant angular velocity ) , , ( y ω ? (5 pts) f. What is the kinetic energy of the system when it is spinning around its C.M. at constant angular velocity ) , , ( y (5 pts)? g. Repeat (e)(f) for an angular velocity ) , , ( z (5 pts). l m 2...
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