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An Introduction To Mechanics

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Problem Set 11 Physics 116 : Due FRIDAY, 04/18/2008 1. In this problem, we will learn about stable and unstable axes of rotation. Consider a rectangular plate of mass M and uniform density σ kg / m 2 , ignoring the thickness of the plate. The center of mass of the book is sitting at the origin and the book is lying in the xy plane. The long axis of the plate has a length 2 a and is parallel to the x axis and the short axis of plate has length a and is lying along the y axis. a) Find the components of the moment of inertia of the plate along its principal axes b) Consider some angular velocity = ω x ˆ x + ω y ˆ y + ω z ˆ z , where one of the components is much greater than the other components, ω a ˆ a . Now calculate the quantity 2 K R I a - | ~ L 2 | , where K R is the rotational kinetic energy, | ~ L 2 | is the total angular momentum, and I a is the moment of inertia about axis
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Unformatted text preview: a . By calculating 2 K R I a-| ~ L 2 | for each of the different principal axes, x , y , and z , can you explain why one axis is an unstable axis of rotation, while the other two are stable? 2. K&K, Problem 7.3 3. K&K, Problem 7.4 4. K&K, Problem 7.6. 5. K&K, Problem 12.1 6. K&K, Problem 12.2 7. K&K, Problem 12.5 8. Extra Credit Question Please work on this question by yourself! A bike wheel of radius r rolls on the ground and a camera (stationary with respect to the ground) takes a picture of the wheel. Due to the motion of the wheel, most of the spokes appear blurred, but there are a set of points where the picture is not blurred at all. Describe the locus of points where the picture appears perfectly sharp....
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