kesavan Posts: 118, Reputation: 1 Junior Member #1 Apr 4, 2017, 06:48 AM
Rotating disk
R radius of circular disk with mass m with initial velocity v and an angular velocity w comes into contact with the ground as shown in the figure. Friction is not negligible, so both the velocity and angular velocity of the disk changes. What is the critical velocity (VC) when the comes to instantaneous rest (in terms of angular velocity wc and R)

 ebaines Posts: 12,131, Reputation: 1307 Expert #2 Apr 4, 2017, 08:49 AM
We won't do homework for you. Please try your hands at this, post back with your attempt, and we'll help you if you are stuck. I suggest you start with basic equations such as $F=ma$ and $T = I \alpha$.
 kesavan Posts: 118, Reputation: 1 Junior Member #3 Apr 4, 2017, 09:24 AM
what theory is applied when this critical position?
Is centre of mass's resultant velocity is zero? ( Vc=Rwc​ )
 ebaines Posts: 12,131, Reputation: 1307 Expert #4 Apr 4, 2017, 09:49 AM
Over some period of time the angular velocity slows to zero due to friction forces. While that is occurring the velocity V is also slowing, due to that same friction force. You are asked to determine the change in velocity that results from friction forces necessary to cause omega to become zero. At that instant the disc is sliding along thee surface but not rotating.
 kesavan Posts: 118, Reputation: 1 Junior Member #5 Apr 4, 2017, 05:53 PM
Question is at critical position, at this instant linear velocity vc and angular velocity wc given in the question (not zero).
 ebaines Posts: 12,131, Reputation: 1307 Expert #6 Apr 5, 2017, 07:29 PM
Please restate the question, precisely as it was originally posed to you. The question as first posed was: "What is the critical velocity (VC) when the comes to instantaneous rest (in terms of angular velocity wc and R)" I assume the word "disk" was left out by mistake (should be "....when the disk comes to instantaneous rest ..."). You haven't defined what "instantaneous rest" means, but given that you asked about velocity at that point it would appear that perhaps w is zero but ve is not. But from your latest post it seems the question should have been: "what is the critical position when the disk comes to instantaneous rest," which I would assume means the point when both v and w are zero. Is that correct?

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