# Doubt on the application of conservation of angular momentum

The following is the picture from the you tube channel physics desmos. In this the man is demonstrating the conservation of angular momentum.

Now the explanation of it is also given in my book as follows, Since the net torque on the body is zero as the body is symmetric about the axis of rotation, the angular momentum is constant. And further is goes that, $$L=Iw=\text{constant}$$ For a constant angular momentum as we increase the radius by expanding out our hands, increases the moment of inertia causing a decrease in angular velocity and as we contract our hands the angular velocity increases. I did understand the explanation. But,

MY QUESTION:-

$$(1)$$- Why is net torque zero?

$$(2)$$- What is the role of symmetry about the axis of rotation in these concerns?

$$(3)$$- Why is the angular momentum not 0? Because if I can find $$r×p$$ at a point, then i can find another point which is $$-r×p$$ diametrically opposite to it?

I posted the same question a while ago but not received well due to my poor communication i believe.

The net torque is zero since the torque is defined as the external force $$f$$ contracted as a vector product with the position $$r$$. That is

$$\tau = r\wedge x$$

We choose the origin of the coordinate at some point along the axis of rotation - the picture for example at the feet of the experimenter. The wedge product of two vector is zero if they are parallel. The only external force is the gravitational force, which is applied to the centre of mass of the experimenter. To be stable his centre of mass is on the line of rotation. Thus, $$x$$ and $$r$$ are parallel, their wedge product is zero and no net torque exists.

I am not sure I understand question 2. There is no symmetry about the axis of rotation. You can see this from the fact that the weights that the experimenter holds are not rings around the axis of rotation. They are two (to an approximation) point masses. The system is clearly not invariant under a rotation along the axis of rotation.

• Are you sure that the only external force is the force due to gravity? Apr 10, 2022 at 17:30