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solutions 17 - Patel Kinal Homework 17 Due Nov 6 2007 7:00...

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Patel, Kinal – 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 – fnd 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 0 = 18 m / s (perpendicular to the cylinder’s axis) ±ies 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: 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 fxed axis but it keeps this axis fxed. 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 = × m~v 0 . Both the radius-vector 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 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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solutions 17 - Patel Kinal Homework 17 Due Nov 6 2007 7:00...

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