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Unformatted text preview: Patel (sap785) homework #8 shubeita (58645) 1 This printout should have 9 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points The position vector of a particle of mass 2 kg is given as a function of time by vectorr = (7 m) + (4 m / s) t . Determine the magnitude of the angular momentum of the particle with respect to the origin at time 6 s . Correct answer: 56 kg m 2 / s. Explanation: Let : vectorr = x + y , x = 7 m , y = v y t = (4 m / s) t, and t = 6 s . Basic Concepts: vector L = vectorr vectorp Solution: vectorv = vectorr t = v y = (4 m / s) . vector L = vectorr vectorp = m vectorr vectorv = m vectorr vectorr t = m ( vectorx + vectory ) vectorv = m xv y k = (2 kg) (7 m) (4 m / s) k = 56 kg m 2 / s k , and is constant as a function of time since = 0 . 002 10.0 points A solid cylinder of mass M = 11 kg, radius R = 0 . 33 m and uniform density is pivoted on a frictionless axle coaxial with its symmetry axis. A particle of mass m = 2 . 2 kg and initial velocity v = 16 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: 13 . 8528 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 vector L before part = vectorr vector P = vectorr mvectorv ....
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This note was uploaded on 04/16/2010 for the course PHY 317k taught by Professor Kopp during the Spring '07 term at University of Texas.
 Spring '07
 KOPP

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