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

• Krushnaraj Pandya
In summary, the rod has no torque about its hinge point, but when the ball hits it, it imparts a non-zero torque. The angular momentum of the system (rod + ball) is conserved.
Krushnaraj Pandya
Gold Member

## 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

Krushnaraj Pandya said:
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.

Doc Al said:
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??

Krushnaraj Pandya said:
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.

Doc Al said:
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

Doc Al said:
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)

Krushnaraj Pandya said:
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.

Doc Al said:
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

## 1. How does the net torque become zero about the hinge of a rod in a ball rod system?

The net torque becomes zero about the hinge of a rod in a ball rod system when the forces acting on the rod are balanced and there is no rotational acceleration.

## 2. What is the significance of having a net torque of zero about the hinge in a ball rod system?

A net torque of zero about the hinge in a ball rod system indicates that the system is in rotational equilibrium, meaning that the rod will not rotate or move unless an external force is applied.

## 3. What factors affect the net torque about the hinge in a ball rod system?

The net torque about the hinge in a ball rod system is affected by the magnitude and direction of the forces acting on the rod, as well as the location of the forces relative to the hinge.

## 4. Can the net torque about the hinge in a ball rod system ever be non-zero?

Yes, the net torque about the hinge in a ball rod system can be non-zero if the forces acting on the rod are unbalanced, resulting in a rotational acceleration.

## 5. How can the net torque about the hinge in a ball rod system be calculated?

The net torque about the hinge in a ball rod system can be calculated by multiplying the force acting on the rod by the perpendicular distance from the force to the hinge, and then summing all of the torques acting on the rod.

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