Angular momentum of a rotating skew rod

  • Thread starter Pushoam
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  • #1
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Homework Statement


upload_2017-8-22_16-54-12.png

upload_2017-8-22_16-54-35.png


Homework Equations




The Attempt at a Solution


The angular momentum of the upper particle is given as
## \vec L_u = m \vec r \times ( \vec \omega \times \vec r )= m[ \vec \omega r^2 - \vec r ( \vec r . \vec \omega )] = m[ r^2 \vec \omega - \omega r \cos \alpha \vec r ]##
The angular momentum of the lower particle is same to that of the upper particle.
Hence, ##\vec L = 2 \vec L_u ##
Is this correct so far?
 

Answers and Replies

  • #2
haruspex
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Homework Statement


View attachment 209494
View attachment 209495

Homework Equations




The Attempt at a Solution


The angular momentum of the upper particle is given as
## \vec L_u = m \vec r \times ( \vec \omega \times \vec r )= m[ \vec \omega r^2 - \vec r ( \vec r . \vec \omega )] = m[ r^2 \vec \omega - \omega r \cos \alpha \vec r ]##
The angular momentum of the lower particle is same to that of the upper particle.
Hence, ##\vec L = 2 \vec L_u ##
Is this correct so far?
Check your expansion of ##\vec r . \vec \omega ##.
 
  • #3
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Check your expansion of ⃗r.⃗ωr→.ω→\vec r . \vec \omega .
After correction:
##
\vec L_u = m \vec r \times ( \vec \omega \times \vec r )= m[ \vec \omega r^2 - \vec r ( \vec r . \vec \omega )] = m[ r^2 \vec \omega - \omega r \sin \alpha \vec r ]##
Is this correct?
 
  • #4
haruspex
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After correction:
##
\vec L_u = m \vec r \times ( \vec \omega \times \vec r )= m[ \vec \omega r^2 - \vec r ( \vec r . \vec \omega )] = m[ r^2 \vec \omega - \omega r \sin \alpha \vec r ]##
Is this correct?
Yes.
 
  • #5
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Yes.
But the angular momentum should be perpendicular to ## \vec r ##. Here, I am getting non-zero component in the direction of ##\hat r##.
 
  • #6
haruspex
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But the angular momentum should be perpendicular to ## \vec r ##. Here, I am getting non-zero component in the direction of ##\hat r##.
The other term, ##\vec\omega##, also has a component in the direction of ##\vec r##. The two may cancel.
 
  • #7
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The other term##\vec\omega##, also has a component in the direction of##\vec r##. The two may cancel.
Yes, it gets canceled.
Thanks for the guidance, thanks a lot.
 

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