Rotational Motion & Conservation of Angular Momentum

[anigeo]

A thin spherical shell lying on a rough horizontal floor is hit by a cue in such a way that the line of action of force passes through the centre.so there is no torque and it moves with a linear velocity V and no angular velocity.the linear velo is to be founded when the shell starts purely rolling.
now the question goes whether the principal of conservation of angular momentum is valid here.i don't think so because an external torque due to friction will be acting on it.
[. The shell will move with a velocity nearly equal to v due to this motion a frictional force well act in the
background direction, for which after some time the shell attains a pure rolling. If we
consider moment about A(the point of contact with the floor), then it will be zero. Therefore, Net angular momentum
about A before pure rolling = net angular momentum after pure rolling.]
This is what my textbook says but it makes me wonder.

 

[Doc Al]

now the question goes whether the principal of conservation of angular momentum is valid here.i don't think so because an external torque due to friction will be acting on it.

Note that they are taking moments about a point of contact with the floor. What's the torque about that point due to friction?

The angular momentum about the center of mass is certainly not conserved.

 

[anigeo]

Note that they are taking moments about a point of contact with the floor. What's the torque about that point due to friction?

The angular momentum about the center of mass is certainly not conserved.

so could u please give me some idea how should i try to solve it?

 

[Doc Al]

so could u please give me some idea how should i try to solve it?

Well, how about using conservation of angular momentum, as suggested by your text?

Set the initial angular momentum (when the sphere is just translating at speed V) equal to the final angular momentum (when it's rolling without slipping).

 

[PJC01]

I would like to clarify that the principle of conservation of angular momentum is still valid in this scenario. While there is a frictional force acting on the shell, it does not generate an external torque as the line of action of the force passes through the center of the shell. This means that the angular momentum of the system is still conserved as there are no external torques acting on it.

The concept of pure rolling also plays a role here. When the shell starts to roll, the frictional force acts in the opposite direction to the linear velocity, causing deceleration. However, this deceleration also results in an increase in the angular velocity of the shell, maintaining the conservation of angular momentum.

In summary, the principle of conservation of angular momentum is still valid in this scenario as there are no external torques acting on the system and the concept of pure rolling allows for the conservation of both linear and angular momentum.