ps9 - PHY 504 Problem Set#9 due 5 November 2010 1 Show that...

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PHY 504 Problem Set #9 due 5 November 2010 1. Show that ε ijk is invariant under rotations, assuming that it transforms as a 3- index tensor: ε ʹஒ i ʹஒ j ʹஒ k = A ʹஒ i i A ʹஒ j j A ʹஒ k k ε ijk 2. A solid rectangular block has sides a , b , and c (a) Calculate the inertia tensor about one of its corners. (b) Find the principal axes and moments. 3. Derivation 5.7. 4. A molecule consists of three equal-mass atoms located at the corners of a rigid equilateral triangle of side a . (a) Calculate the inertia tensor of the molecule about its center of mass, in the body-fixed frame. (b) Describe the motion of the molecule in the body-fixed frame, and in particular find the shape of the polhode. What is the angular frequency of the precession of the axis of rotation?
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