Conservation of Angular Momentum Conceptual Question

[leeone]

3. A metal bar is hanging from a hook in the ceiling
when it is suddenly struck by a ball that is moving
horizontally (see figure). The ball is covered with
glue, so it sticks to the bar. The collision takes place
over a very short time span. During this collision
a) the angular momentum of the system (ball and bar) is conserved about the hook because only gravity is acting on the system.
b) the angular momentum of the system (ball and bar) is not conserved because the hook exerts a force on the bar.
c) the angular momentum of the system (ball and bar) is conserved about the hook because neither the hook nor gravity exerts any torque on this system about the hook.
d) both the angular momentum of the system (ball and bar) and its kinetic energy are conserved.
e) both the linear momentum and the angular momentum of the system (ball and bar) are conserved.
4.

I know the answer is c, but I don't know why linear momentum is not conserved...

 

[TSny]

In general, what causes the linear momentum of a system not to be conserved?

 

[leeone]

An external force on the system

 

[TSny]

Yes. Can you identify a horizontal external force on the bar-ball system during the collision?

 

[leeone]

http://hyperphysics.phy-astr.gsu.edu/hbase/class/phscilab/balpen.html

Okay so I am assuming the hook is exerting the horizontal force on the bar-ball system? I posted the link above because I am confused if it would matter if the pivot point was frictionless...would linear momentum be conserved as they say in the link above?

 

[TSny]

Okay so I am assuming the hook is exerting the horizontal force on the bar-ball system?

Yes, that's right

I posted the link above because I am confused if it would matter if the pivot point was frictionless...would linear momentum be conserved as they say in the link above?

Friction in the pivot is not important during the collision, assuming that the friction is not huge.

The ballistic pendulum of the type shown in your link is kind of special. The pendulum is constructed with almost all of its mass concentrated in the bob. So, you can approximate this pendulum as a simple pendulum. Then you can show that conservation of angular momentum about the pivot during the collision implies that linear momentum is also conserved during the collision (assuming a completely inelastic collision). The horizontal external force at the pivot during the collision in this system is negligible.

But for a physical pendulum like a bar, the external, horizontal reaction force at the pivot is not negligible and linear momentum of the ball and bar are not conserved during the collision. (Unless the ball happens to strike the bar at a special point called the center of percussion. Then there would be no external horizontal reaction force at the pivot.)