Chp. 10 - 961 Chapter 10 Angular Momentum Conceptual...

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Unformatted text preview: 961 Chapter 10 Angular Momentum Conceptual Problems 1 True or false: ( a ) If two vectors are exactly opposite in direction, their cross product must be zero. ( b ) The magnitude of the cross product of 2 vectors is at a minimum when the two vectors are perpendicular. ( c ) Knowing the magnitude of the cross product of two nonzero vectors and their individual magnitudes uniquely determines the angle between them. Determine the Concept The cross product of vectors A G and B G is defined to be n AB B A ˆ sin φ = × G G where n ˆ is a unit vector normal to the plane defined by A G and B G . ( a ) True. If A G and B G are in opposite direction, then sin φ = sin(180 ° ) = 0 . ( b ) False. If A G and B G are perpendicular, then sin φ = sin(90 ° ) = 1 and the cross product of A G and B G is a maximum. ( c ) False. × = AB B A G G 1 sin φ , because of the magnitude of B A G G × , gives the reference angle associated with B A G G × . 2 Consider two nonzero vectors G A and G B . Their cross product has the greatest magnitude if G A and G B are ( a ) parallel, ( b ) perpendicular, ( c ) antiparallel, ( d ) at an angle of 45° to each other. Determine the Concept The cross product of the vectors A G and B G is defined to be n AB B A ˆ sin φ = × G G where n ˆ is a unit vector normal to the plane defined by A G and B G . Hence, the cross product is a maximum when sin φ = 1. This condition is satisfied provided A G and B G are perpendicular . ) ( b is correct. 3 What is the angle between a force F G and a torque vector τ G produced by F G ? Determine the Concept Because n rF F r ˆ sin φ τ = × = G G G , where n ˆ is a unit vector normal to the plane defined by r G and F G , the angle between F G and τ G is . 90 ° Chapter 10 962 4 A particle of mass m is moving with a constant speed v along a straight line that passes through point P . What can you say about the angular momentum of the particle relative to point P ? ( a ) Its magnitude is mv . ( b ) Its magnitude is zero. ( c ) Its magnitude changes sign as the particle passes through point P . ( d ) It varies in magnitude as the particle approaches point P . Determine the Concept L G and p G are related according to . p r L G G G × = Because the motion is along a line that passes through point P , r = 0 and so is L . ) ( b is correct. 5 [SSM] A particle travels in a circular path and point P is at the center of the circle. ( a ) If the particles linear momentum G p is doubled without changing the radius of the circle, how is the magnitude of its angular momentum about P affected? ( b ) If the radius of the circle is doubled but the speed of the particle is unchanged, how is the magnitude of its angular momentum about P affected? ...
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