Angular Momentum and Velocity

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Homework Statement


A rotating uniform-density disk of radius 0.6 m is mounted in the vertical plane. The axle is held up by supports that are not shown, and the disk is free to rotate on the nearly frictionless axle. The disk has mass 5.8 kg. A lump of clay with mass 0.5 kg falls and sticks to the outer edge of the wheel at location A, < -0.36, 0.480, 0 > m. (Let the origin of the coordinate system be the center of the disk.) Just before the impact the clay has a speed 8 m/s, and the disk is rotating clockwise with angular speed 0.83 radians/s.



1) Just before the impact, what is the angular momentum of the combined system of wheel plus clay about the center C? (As usual, x is to the right, y is up, and z is out of the screen, toward you.)
LC,i = ???kg · m2/s

2) Just after the impact, what is the angular momentum of the combined system of wheel plus clay about the center C?
LC,f = ???kg · m2/s

3) Just after the impact, what is the angular velocity of the wheel?
omega vecf = ???radians/s


Homework Equations


I have no clue


The Attempt at a Solution


I don't know how to do it
 

Answers and Replies

  • #2
haruspex
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1) Just before the impact, what is the angular momentum of the combined system of wheel plus clay about the center C? (As usual, x is to the right, y is up, and z is out of the screen, toward you.)
LC,i = ???kg · m2/s
Angular momentum has units like kg.m/s.
The angular momentum of the combined system about C is the sum of the individual angular momenta about C.
What is the moment of inertia of the disc about its centre?
 
  • #3
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I=.5*m*r^2
=.5*5.8*.6^2
=1.044
 
  • #4
haruspex
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I=.5*m*r^2
=.5*5.8*.6^2
=1.044
Right, but don't forget to include units.
You know the initial rate of rotation of the disc, so what is its angular momentum about its centre?
 

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