How is net torque zero about hinge of rod in ball rod system

[Krushnaraj Pandya]

Homework Statement

There are 2 situations-
1)a rod of length L is lying on a smooth horizontal surface with its one end hinged to the ground, a ball traveling with a velocity v hits its other end and comes to rest, How is the net external torque about hinge point O zero?
2) in the second case, the same rod is lying on the same surface but it is not hinged and is free to move, the same ball hits it again- how is the net torque about center of rod zero?

3. The Attempt at a Solution
I understand that in the first case torque of hinge force about hinge is zero, but when the ball hits the rod it'll impart a non zero torque about O- how is the angular momentum conserved about O then?
In the second case, the ball should again provide a torque about COM, also why isn't torque about any other point also zero since the rod isn't hinged in the second case

 

[Doc Al]

I understand that in the first case torque of hinge force about hinge is zero, but when the ball hits the rod it'll impart a non zero torque about O- how is the angular momentum conserved about O then?

The angular momentum of the system (rod + ball) is conserved -- not the angular momentum of the rod alone.

 

[Krushnaraj Pandya]

The angular momentum of the system (rod + ball) is conserved -- not the angular momentum of the rod alone.

My textbook says "angular momentum is conserved when there is no net external torque on the system" how can we define net external torque for two different bodies in the system and decide whether it is zero??

 

[Doc Al]

My textbook says "angular momentum is conserved when there is no net external torque on the system" how can we define net external torque for two different bodies in the system and decide whether it is zero??

If you treat the rod + ball as a system, are there any external forces in the problem? (Other than that provided by the hinge, which exerts no torque.) Consider Newton's 3rd law.

 

[Krushnaraj Pandya]

If you treat the rod + ball as a system, are there any external forces in the problem? (Other than that provided by the hinge, which exerts no torque.) Consider Newton's 3rd law.

Ah! ok, got it

 

[Krushnaraj Pandya]

If you treat the rod + ball as a system, are there any external forces in the problem? (Other than that provided by the hinge, which exerts no torque.) Consider Newton's 3rd law.

Then in the second case shouldn't AM be conserved about any point on the rod? since there is no hinge to worry about and no external forces (keeping in mind Newtons 3rd law)

 

[Doc Al]

Then in the second case shouldn't AM be conserved about any point on the rod? since there is no hinge to worry about and no external forces (keeping in mind Newtons 3rd law)

You can certainly choose any fixed point (fixed in the "lab" frame) to apply conservation of angular momentum. But one must be careful about applying it to moving points, such as arbitrary points fixed to the rod. The center of mass of the system has special properties that allow it to always be used as your axis.

 

[Krushnaraj Pandya]

You can certainly choose any fixed point (fixed in the "lab" frame) to apply conservation of angular momentum. But one must be careful about applying it to moving points, such as arbitrary points fixed to the rod. The center of mass of the system has special properties that allow it to always be used as your axis.

I understand, thank you