Angular velocity and regular velocity

[asi123]

Homework Statement

I have this pole with mass M and length L which is on a flat table with no friction. Another particle, which has the same mass M hits him on its edge with velocity V, which is vertical to the pole.
then, the particle sticks to the pole and they move together.
I need to find both the Angular velocity and the regular velocity of the new body.
My question is about the regular velocity, can I use the conservation of linear momentum law and say that mv = 2mv', and to find the regular velocity?
10x.

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

My question is about the regular velocity, can I use the conservation of linear momentum law and say that mv = 2mv', and to find the regular velocity?

Hi asi123!

Yes, you're right!

You can always use conservation of linear momentum in a direction if there are no external forces in that direction, because that's simply good ol' Newton's second law with a net force of zero.

Since there is no friction in this case, and the only external force is gravity, which is vertical, conservation of horizontal momentum will apply.

(don't forget that the centre of mass will be in a different place, of course)

 

[asi123]

10x.