hw5 - Homework 5 PHY 354S Advanced Classical Mechanics Due...

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Unformatted text preview: Homework 5, PHY 354S, Advanced Classical Mechanics Due on Monday, March 22, 2010 in class. 1. Moments of inertia 1. Find the principal axes and moments of inertia of a flat homogeneous rectangular body ( | x | ≤ a , | y | ≤ b ) of mass m . 2. Find the frequency of small oscillations of a compound pendulum—a rigid body of mass μ swinging about a fixed horizontal axis in the gravitational field of the Earth. Let the angles between the axis of oscillations and the principal axes of inertia be α, β, γ , the principal moments of inertia be I 1 , I 2 , I 3 , and l be the distance between the center of mass and axis of rotation. Finish up this problem if there is not enough time during the tutorial. 3. Show that the principal moments of inertia of an arbitrary body obey the triangle inequalities: I 1 ≤ I 2 + I 3 , I 2 ≤ I 3 + I 1 , I 3 ≤ I 2 + I 1 , and that an equality can only occur for a flat body....
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