Chap 10 SM - Chapter 10 Angular Momentum Conceptual...

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969 Chapter 10 Angular Momentum Conceptual Problems 1 True or false: ( a ) If two vectors are exactly opposite in direction, their vector product must be zero. ( b ) The magnitude of the vector product of two vectors is at a minimum when the two vectors are perpendicular. ( c ) Knowing the magnitude of the vector product of two nonzero vectors and the vectors individual magnitudes uniquely determines the angle between them. Determine the Concept The vector product of A r and B r is defined to be n B A ˆ sin φ AB = × r r where n ˆ is a unit vector normal to the plane defined by A r and B r and is the angle between A r and B r . ( a ) True. If A r and B r are in opposite direction, then sin = sin 180 ° = 0 . ( b ) False. If A r and B r are perpendicular, then sin = sin 90 ° = 1 and the vector product of A r and B r is a maximum. ( c ) False. Knowing the magnitude of the vector product and the vectors individual magnitudes only gives the magnitude of the sine of the angle between the vectors. It does not determine the angle uniquely, nor does this knowledge tell us if the sine of the angle is positive or negative. 2 Consider two nonzero vectors r A and r B . Their vector product has the greatest magnitude if r A and r B are ( a ) parallel, ( b ) perpendicular, ( c ) antiparallel, ( d ) at an angle of 45° to each other. Determine the Concept The vector product of the vectors A r and B r is defined to be n B A ˆ sin AB = × r r where n ˆ is a unit vector normal to the plane defined by A r and B r and is the angle between A r and B r . Hence, the vector product of A r and B r is a maximum when sin = 1. This condition is satisfied provided A r and B r are perpendicular . ) ( b is correct.
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Chapter 10 970 3 What is the angle between a force vector F r and a torque vector τ r produced by F r ? Determine the Concept Because n F r τ ˆ sin φ rF = × = r r r , where n ˆ is a unit vector normal to the plane defined by r r and F r , the angle between F r and r is . 90 ° 4 A point 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 r and p r are related according to p r L r r r × = and the magnitude of L r is sin rp L = where is the angle between r r and p r . 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 particle’s linear momentum p r 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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Chap 10 SM - Chapter 10 Angular Momentum Conceptual...

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