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ism_chapter_10

# ism_chapter_10 - Chapter 10 Conservation of Angular...

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735 Chapter 10 Conservation of Angular Momentum Conceptual Problems *1 ( a ) True. The cross product of the vectors A r and B r is defined to be . ˆ sin n B A φ AB = × r r If A r and B r are parallel, sin φ = 0 . ( b ) True. By definition, ω r is along the axis. ( c ) True. The direction of a torque exerted by a force is determined by the definition of the cross product. 2 Determine the Concept The cross product of the vectors A r and B r is defined to be . ˆ sin n B A φ AB = × r r Hence, the cross product is a maximum when sin φ = 1. This condition is satisfied provided A r and B r are perpendicular . correct. is ) ( c 3 Determine the Concept L r and p r are related according to . p r L r r r × = From this definition of the cross product, L r and p r are perpendicular; i.e., the angle between them is 90 ° . 4 Determine the Concept L r and p r are related according to . p r L r r r × = Because the motion is along a line that passes through point P , r = 0 and so is L . correct. is ) ( b *5 •• Determine the Concept L r and p r are related according to . p r L r r r × = ( a ) Because L r is directly proportional to : p r . doubles Doubling L p r r ( b ) Because L r is directly proportional to : r r . doubles Doubling L r r r

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Chapter 10 736 6 •• Determine the Concept The figure shows a particle moving with constant speed in a straight line (i.e., with constant velocity and constant linear momentum). The magnitude of L is given by rp sin φ = mv ( r sin φ ). Referring to the diagram, note that the distance r sin φ from P to the line along which the particle is moving is constant. Hence, mv ( r sin φ ) is constant and so constant. is L r 7 False. The net torque acting on a rotating system equals the change in the system’s angular momentum; i.e., dt dL = net τ , where L = I ω . Hence, if net τ is zero, all we can say for sure is that the angular momentum (the product of I and ω ) is constant. If I changes, so must ω . *8 •• Determine the Concept Yes, you can. Imagine rotating the top half of your body with arms flat at sides through a (roughly) 90 ° angle. Because the net angular momentum of the system is 0, the bottom half of your body rotates in the opposite direction. Now extend your arms out and rotate the top half of your body back. Because the moment of inertia of the top half of your body is larger than it was previously, the angle which the bottom half of your body rotates through will be smaller, leading to a net rotation. You can repeat this process as necessary to rotate through any arbitrary angle. 9 Determine the Concept If L is constant, we know that the net torque acting on the system is zero. There may be multiple constant or time-dependent torques acting on the system as long as the net torque is zero. correct. is ) ( e 10 •• Determine the Concept No. In order to do work, a force must act over some distance. In each inelastic collision the force of static friction does not act through any distance.
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