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I had this question on my physics final this summer and I can't figure out the answer. A uniform hoop of mass M and radius R is hanging from a frictionless pivot point. A sticky putty ball is thrown horizontally at the hoop with linear momentum "mVo", where m is the mass of the putty and "Vo" is initial velocity. The putty sticks to the hoop in such a way that a line drawn from the putty to the center of the hoop is parallel to the horizontal.

Find the angular speed of the hoop imidiately after impact.

Find the minimum mass m of the putty ball so that the hoop is able to complete a full vertical "loop" around it's pivot point.

Now I tried thinking about this problem and I know that since the putty ball sticks to the hoop, mechanical energy is not conserved. At the time of impact, angular momentum is not conserved in the putty-hoop system dbecause the pivot point exerts an outside force. Also, linear momentum is not conserved because the pivot exerts and outside force also. (please tell me if my thinking is incorrect with any of these)

From there, I'm stuck, because I dont know what conservation laws to apply and I also dont know how linear impulse of angular-impulse would help me either, but one of these methods MUST work (I hope)

Here is a link to an image of the problem.

http://img316.imageshack.us/img316/5499/hooputty9am.jpg [Broken]

Find the angular speed of the hoop imidiately after impact.

Find the minimum mass m of the putty ball so that the hoop is able to complete a full vertical "loop" around it's pivot point.

Now I tried thinking about this problem and I know that since the putty ball sticks to the hoop, mechanical energy is not conserved. At the time of impact, angular momentum is not conserved in the putty-hoop system dbecause the pivot point exerts an outside force. Also, linear momentum is not conserved because the pivot exerts and outside force also. (please tell me if my thinking is incorrect with any of these)

From there, I'm stuck, because I dont know what conservation laws to apply and I also dont know how linear impulse of angular-impulse would help me either, but one of these methods MUST work (I hope)

Here is a link to an image of the problem.

http://img316.imageshack.us/img316/5499/hooputty9am.jpg [Broken]

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