Conservation of angular and linear momentum

[Nikitin]

Homework Statement

http://home.phys.ntnu.no/brukdef/undervisning/tfy4145/ovinger/Ov10.pdf
Look at the picture in "oppgave 1".

Suppose you have an incoming mass which hits the very thin rod straight on in a completely inelastic collision. the incoming mass is $m$, the rod has a mass of $M$, and the little mass hits the rod at a length $l$ from the top.

According to the text, the linear momentum right before and right after are NOT preserved, while the angular momentum is.

The Attempt at a Solution

I calculated the total linear momentum before and after, and indeed I got:

$$p_0 = m v$$
and
$$p_1 = \frac{m v + M L/2l}{MvL^2 /3ml^2 +1}$$

so the two momentums are seemingly unpreserved. Why is this so? I realize it's a translational motion going over to a rotational one, but what does this have to do with linear momentum not being preserved??

 

[voko]

You forgot to mention that the rod is hinged at its top. What is the implication of that?

 

[Nikitin]

That the motion after the collision is rotational?

 

[voko]

That too. But on a more fundamental level, conservation of momentum works only when no external forces act on the system. Is that the case with the hinged rod?

 

[Nikitin]

ahh, of course. How stupid of me. thanks for the help :)