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Unformatted text preview: PHYS 310: Exam3 November 18, 2011 Name: Problem 1 (30 points) A circular hoop of radius a swings as a physical pendulum about a point on the circumference. Find the period of oscillation for small amplitude if the axis of rotation is: (a) (15 points) Normal to the plane of the hoop (b) (15 points) In the plane of the hoop. (a) 2 cm I ma ⊥ = (all mass in rim) 2 2 2 2 rim I ma ma ma ⊥ = + = 2 2 2 rim I a T mga g π π ⊥ ∴ = = (b) 2 2 z x y cm I I I I ma = + = = P ( 29 cm I ⊥ = 2 2 cm ma I ∴ = P hence 2 2 2 3 2 2 rim ma I ma ma = + = P 3 2 2 2 rim I a T mga g π π ∴ = = P PHYS 310: Exam3 November 18, 2011 Name: Problem 2 (30 points) A ball is projected without initial rotation, at speed v up a rough inclined plane of inclination θ and coefficient of sliding friction μ k . Find the position of the ball as a function of time, and determine the position of the ball when pure rolling begins. Assume that μ k >2/7 tan θ . (Hint: the ball begins pure rolling when v a ϖ = )....
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This note was uploaded on 12/07/2011 for the course PHYS 310 taught by Professor Jones,m during the Fall '08 term at Purdue.
 Fall '08
 Jones,M

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