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I have a doubt on the following question which is a very common question in rotational motion A uniform thin rod of length ‘L’ and mass ‘M’ can rotate freely in a horizontal plane. The rod is at rest when a bullet of mass ‘m’ traveling in the rotation plane is fired into one end of the rod. As viewed from above, the bullet's path makes angle ‘θ’ with the rod. If the bullet lodges in the rod and the angular velocity of the rod is ‘w’ immediately after the collision, what is the bullet's speed just before impact? Usually this problem is solved using angular and linear momentum conservation. When the bullet is lodged into the rod the system rotates about the centre of mass since it is free rotation. But I have noticed that none of the books consider the shift in centre of mass when the bullet lodges. Pls help me

I have a doubt on the following question which is a very common question in rotational motion
 
A uniform thin rod of length ‘L’ and mass ‘M’ can rotate freely in a  horizontal plane. The rod is at rest when a bullet of mass ‘m’ traveling in the rotation plane is fired into one end of the rod. As viewed from above, the bullet's path makes angle ‘θ’ with the rod. If the bullet lodges in the rod and the angular velocity of the rod is ‘w’ immediately after the collision, what is the bullet's speed just before impact?
 
Usually this problem is solved using angular and linear momentum conservation. 
When the bullet is lodged into the rod the system rotates about the centre of mass since it is free rotation.
But I have noticed that none of the books consider the shift in centre of mass when the bullet lodges. Pls help me

Grade:12

1 Answers

Abhishek Kumar
askIITians Faculty 255 Points
7 years ago
If you consider bullet and rod as system, the force of interaction is internal. So, COM of the system doesn’t change but definitely the COM of the rod changes.

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