On a horizontal smooth plane there is a fixed vertical cylinder and a particle A connected to the cylinder by a thread AB. The particle is set in motion with the initial velocity v as shown in the figure. Is there any fixed point relative to which the angular

momentum of the particle is constant in the process of motion?

Explanation

The only force acting on the particle A in this case is the tension `vecT` of the thread. It is easy to see that there is no point here relative to which the torque of the tension is always zero. Therefore, there is no point relative to which the angular momentum of the particle would be constant. The tension acting on the particle is along the string. Thus, any point lying on the line of string, will have zero torque due to tension, about itself. Since particle is moving, this line keeps on changing.
This example illustrates that sometimes a point relative to which the angular momentum of a particle is constant cannot be found at all.