Page1 / 80

Chp. 10 - Chapter 10 Angular Momentum Conceptual Problems 1...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon

Chp. 10 - Chapter 10 Angular Momentum Conceptual Problems 1...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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 = sin(180 ° ) = 0 . ( b ) False. If A G and B G are perpendicular, then sin = 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 , 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 = × 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 = 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 = × = 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 G is . 90 °
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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 particle’s 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? Determine the Concept L G and p G are related according to . p r L G G G × = ( a ) Because L G is directly proportional to p G , L is doubled.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.
Ask a homework question - tutors are online