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Rotational Mechanics

Rotational Mechanics

by Anshul Chanchlani -
Number of replies: 2

A vertically oriented uniform rod of mass M and lenght l can rotate about its upper end. A horizontally flying bullet of mass m strikes the lower end of the rod and gets stuck in it; as a result, the rod swings through an angle alpha. Assume that m<<M, find: (a) the velocity of the flying bullet; (b) the momentum increment in the system "bullet-rod" during the impact, what causes the change of that momentum; (c) at what distance x from the upper end of the rod the bullet must strike for the momentum of the system "bullet-rod" to remain constant during the impact.

 Ans:  a) v=M/m  root ( 2/3 gl) sin alpha/2

         b) change in momentum = M [  ((1/6 gl)^0.5)  sin alpha/2 ]

        c) x=2l/3

Please reply with explanation!

In reply to Anshul Chanchlani

Re: Rotational Mechanics

by Manish Verma -

The rod must be having support from the top and hence due to the reaction force at the top, COLM may not work for the rod+bullet system always (this reaction force from the support is the external force).

This external force passes from the top. Hence, it would not have torqure about the top point. The approach therefore is to go for COAM about the top point just before and just after the collision. Subsequently, you can apply COME.

If you still have problem with this, you can post it specifically.