ff - Patel(sap785 homework#8 shubeita(58645 This print-out...

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Patel (sap785) – homework #8 – shubeita – (58645) 1 This print-out should have 9 questions. Multiple-choice 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) ˆ ı + (4 m / s) t ˆ  . 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 ˆ ı + y ˆ  , 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) ˆ  . vector L = vectorr × vectorp = m vectorr × vectorv = m vectorr × ∂vectorr ∂t = m ( vectorx ˆ ı + vectory ˆ ) × vectorv ˆ = m x v y ˆ k = (2 kg) (7 m) (4 m / s) ˆ k = 56 kg m 2 / s ˆ k , and is constant as a function of time since ˆ × ˆ = 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 0 = 16 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: 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 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 vector L before part = vectorr × vector P 0 = vectorr × mvectorv 0 .
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