Momentum Conservation: Ball Hitting Pivoted Rod

[Zubair Ahmad]

If a ball hits a rod at the top which is pivoted at bottom end then is linear momentum conserved?

 

[Nugatory]

If a ball hits a rod at the top which is pivoted at bottom end then is linear momentum conserved?

Both linear and angular momentum are conserved as long as the system is closed (that is, you're considering total for the the ball, the rod, and whatever the other end of the pivot is attached to). If the other end of the pivot is fastened directly or indirectly to the Earth and you are treating the Earth as completely immobile (which is a really good simplifying assumption here) then rod+ball system is not closed, and the forces applied by the pivot to the rod can change both the linear and the angular momentum of that system.

 

[Zubair Ahmad]

But as written in Klepner introduction to mechanics only linear momentum is not conserved.

 

[Ibix]

In this particular case, all the forces @Nugatory is talking about pass through the hinge, so are always radial and don't affect angular momentum about the hinge. So angular momentum is conserved, yes. That isn't generally true, but it is in this case.

 

[jbriggs444]

pass through the hinge, so are always radial and don't affect angular momentum about the hinge

If you are using the hinge as the axis about which angular momentum is calculated than no force at the hinge (radial or otherwise) can ever affect angular momentum. The moment arm is zero. The force at the hinge is not limited to being in the radial direction. The hinge can and will produce a shear force just as easily. Hence wheelbarrows.

 

[Nugatory]

But as written in Klepner introduction to mechanics only linear momentum is not conserved.

I said "can change", not "will change". Whether this interaction will conserve angular momentum or not depends on what assumptions you make about the detailed behavior of the pivot; a textbook like K&K will typically assume an idealized pivot and in that case angular momentum will be conserved.