What is the value of vp for a particle ejected from a rotating rod?

AI Thread Summary
The discussion focuses on calculating the speed of a particle ejected from a rotating rod. The rod has a length of 0.790 m and rotates at an angular speed of 22.0 rad/s. The particle, with a mass of M/3.00, is ejected perpendicularly from the rod and has a speed vp that is 6.00 m/s greater than the rod's end speed at the moment of ejection. Participants are attempting to set up the problem using conservation of angular momentum, but face challenges in determining the correct initial conditions for the particle. The key to solving the problem lies in applying the principles of angular momentum and understanding the relationship between the rod's motion and the ejected particle's speed.
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The figure below is of an overhead view of a thin uniform rod of length 0.790 m and mass M rotating horizontally at angular speed 22.0 rad/s about an axis through its center. A particle of mass M/3.00 attached to one end is ejected from the rod and travels along a path that is perpendicular to the rod at the instant of ejection. If the particle's speed vp is 6.00 m/s greater than the speed of the end of the rod just after ejection, what is the value of vp?
W0245-N.jpg





Li=Lf, L=Iw, l=rmv



The Attempt at a Solution


- I haven't been able to attempt this problem because I'm having problems setting it up. I'm trying to set up the initial side right now and I am using 1/12ML^2 for the rod, but unsure what to use for the particle since it's inside of the rod. I think I can solve the problem if I can get past this step.
 
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Use conservation of angular momentum. The angular momentum of the particle about the center is mvr
 

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