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Unformatted text preview: Patel, Kinal Homework 17 Due: Nov 6 2007, 7:00 pm Inst: D Weathers 1 This printout should have 9 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points A solid cylinder of mass M = 23 kg, radius R = 0 . 34 m and uniform density is pivoted on a frictionless axle coaxial with its symmetry axis. A particle of mass m = 3 . 1 kg and initial velocity v = 18 m / s (perpendicular to the cylinders axis) flies too close to the cylinders edge, collides with the cylinder and sticks to it. Before the collision, the cylinder was not ro tating. What is its angular velocity after the collision? Correct answer: 11 . 2409 rad / s. Explanation: Basic Concept: Conservation of Angu lar Momentum, L particle z + L cylinder z = const . The axle allows the cylinder to rotate without friction around a fixed axis but it keeps this axis fixed. Let the z coordinate axis run along this axis of rotation; then the axle may exert arbitrary torques in x and y directions but z 0. Consequently, the z componenent of the angular momentum must be conserved, L z = const, hence when the particle collides with the cylinder L before z, part + L before z, cyl = L z, net = L after z, part + L after z, cyl . Before the collision, the cylinder did not rotate hence L before z, cyl = 0 while the particle had angular momentum ~ L before part = ~r ~ P = ~r m~v . Both the radiusvector ~r and the velocity ~v of the particle lie in the xy plane ( to the z axis), and according to the picture, at the moment of collision the radius vector has mag nitude  ~r  = R equal to the cylinders radius and direction perpendicular to the particles velocity. Hence, its angular momentum is parallel to the z axis and has magnitude  ~ L before part  = L before z, part = Rmv ....
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This note was uploaded on 10/24/2010 for the course PHYS PHYS 1710 taught by Professor Weathers during the Spring '07 term at North Texas.
 Spring '07
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