# Conservation of Angular momentum during inversion of a rotating wheel

in the picture the person is sitting with a wheel rotating. He just reverses the wheel so that the angular velocity and angular momentum too are inverted. Then according to conservation law the system's angular momentum must be conserved and the man must have an angular momentum. Then what applies the required torque to him and how ? Can this be explained using Newton's laws?

Then what applies the required torque to him and how ? Can this be explained using Newton's laws?

For the rotation of the wheel to change the direction, a torque has to be applied to it by the person's hand. According to the Newton's third law for rotation, the opposite torque will be applied by the wheel to the person's hand, which will cause the angular acceleration of the person.

The first thing to note is that if the angular momentum of the flywheel was large then it is unlikely that the inversion of the flywheel could be done one-handed.
Such demonstrations are often done with lead loaded bicycle wheel with two handles held by hands on either side of the wheel.

There are a number of forces involved in a 3D space so I have had to annotate two diagrams to try and explain what is happening.
First of all the axis of rotation of the flywheel has to be moved from the vertical.
This is done by applying a torque (forces $F1$ and $F2$) to the flywheel as shown in the left hand diagram.
The anticlockwise angular momentum of the flywheel (and person) is changed because the turntable on which the person is standing is not allowed to tip from the horizontal and the ground on which the turntable stands exerts an external torque on the person-flywheel system.

What is conserved is the vertical angular momentum of the person-flywheel system because the turntable with low-friction bearing cannot exert a torque in the vertical direction.

Considering the person-flywheel system forces $G1,\,G2,\,H1$ and $H2$ are all internal forces with $G1$ and $H1$ being Newton third law pairs and likewise with forces $G2$ and $H2$.
The vertical torque on the flywheel due to the hand is equal in magnitude but opposite in direction to the vertical torque on the hand due to the flywheel.

So whatever vertical angular momentum the flywheel loses the person gains ie the vertical angular momentum of the person-flywheel system is conserved.

The actual system of forces is more complicated but I hope you understand the general picture of what is happening?