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Homework_17

# Homework_17 - Nguyen Thanh Homework 17 Due Nov 6 2007 7:00...

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Nguyen, Thanh – Homework 17 – Due: Nov 6 2007, 7:00 pm – Inst: D Weathers 1 This print-out should have 9 questions. Multiple-choice 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 = 18 kg, radius R = 0 . 19 m and uniform density is pivoted on a frictionless axle coaxial with its symmetry axis. A particle of mass m = 2 . 1 kg and initial velocity v 0 = 9 . 1 m / s (perpendicular to the cylinder’s axis) flies too close to the cylinder’s 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: 9 . 06117 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 τ 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 0 = ~r × m~v 0 . Both the radius-vector ~r and the velocity ~v 0 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 cylinder’s radius and direction perpendicular to the particle’s velocity. Hence, its angular momentum is parallel to the z axis and has magnitude | ~ L before part | = L before z, part = Rmv 0 .

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Homework_17 - Nguyen Thanh Homework 17 Due Nov 6 2007 7:00...

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