Cons. of Angular Momentum in Pool

[mikey555]

Homework Statement

On a level billiards table a cue ball, initially at rest at point O on the table, is struck so that it leaves the cue stick with a center-of-mass speed v₀ and a "reverse" spin of angular speed w₀. A kinetic friction force acts on the ball as it initially skids across the table.

Explain why the ball's angular momentum is conserved about point O.

http://session.masteringphysics.com/problemAsset/1058092/3/GIANCOLI.ch11.p52.jpg

Homework Equations

dL/dt = 0, L = constant

The Attempt at a Solution

Here's what confuses me about this problem. When we're working with cons. of angular momentum, we assume that there are no external torques or forces. However, the stick hitting the ball is the primary torque involved. How can we say angular momentum is conserved unless we add the stick (and therefore, the person holding the stick) into the system. But I don't think this problem wants us to do that.

Thanks for the help.

 

[anathema]

I would like to clarify that the conservation of angular momentum is applicable only when there are no external torques acting on the system. In this scenario, the cue ball is initially at rest and is struck by the cue stick with a certain force and spin. This force and spin impart an initial angular momentum to the ball about point O. However, as the ball moves along the table, it experiences a kinetic friction force which acts against its motion. This force does not exert a torque about point O, as it is directed along the direction of motion of the ball. Therefore, the net external torque acting on the ball about point O is zero and hence, the angular momentum of the ball about point O is conserved.

It is important to note that the person holding the cue stick is not a part of the system, and hence, their presence does not affect the conservation of angular momentum. The conservation of angular momentum only applies to the objects within the system, which in this case are the cue ball and the table. Therefore, we can say that the angular momentum of the ball about point O is conserved because there are no external torques acting on it.

I hope this explanation helps to clarify any confusion you may have had. it is important to carefully consider all the forces and torques acting on a system before applying any conservation laws.

 

[nlightner]

I would approach this problem by first defining the system and identifying the external forces acting on it. In this case, the system is the cue ball and the external forces are the friction force and the force from the cue stick.

It is true that the force from the cue stick provides a torque on the cue ball, but this torque is internal to the system. This means that the torque does not come from an external force acting on the system, but rather from a force within the system itself.

In this case, the cue ball and the cue stick are considered as one system, and the internal torque from the stick on the ball does not affect the conservation of angular momentum. This is because the torque from the stick is offset by an equal and opposite torque from the ball on the stick, leading to a net torque of zero.

Therefore, the angular momentum of the system, which is defined as the sum of the angular momentum of each individual component, remains constant. This is in accordance with the conservation of angular momentum, which states that the total angular momentum of a system remains constant in the absence of external torques.

In summary, the ball's angular momentum is conserved about point O because the external forces acting on the system do not contribute to any net torque, allowing for the conservation of angular momentum.