Because people, dumbbells and rotating platforms form a system, the resultant torque is 0. So angular momentum is conserved.

Because L=Jw, j decreases, so w increases. The potential energy of the system is constant and the kinetic energy increases, so the mechanical energy is not conserved.

The law of conservation of angular momentum is one of the universal laws of physics, which reflects the universal law of particle and particle system moving around a point or an axis. It reflects the general law that particles and particle systems move around a fixed point (or axis) when there is no external force or the resultant torque of the external force on the fixed point (or axis) is always equal to zero.

The law of conservation of angular momentum is that for a particle, the law of angular momentum can be expressed as the wechat quotient of angular momentum of the particle to a fixed point against time, which is equal to the moment of the force acting on the particle to the point.

One of the universal laws of physics. For example, a particle moving in a central force field is always subjected to a centripetal force passing through the force center. Because the moment of centripetal force to the force center is zero, according to the angular momentum theorem, the angular momentum of particles to the force center is conserved. So the trajectory of the particle is a plane curve, and the vector diameter from the particle to the force center sweeps the same area in the same time.

Law of conservation of angular momentum;

One of the universal laws of physics. Reflect the general law of particle and particle system moving around a point or an axis.

If the resultant torque is zero (that is, m =0), then L 1=L2, that is, L= constant vector.

That is to say, for a fixed point O, the resultant moment of a particle is zero, so the angular momentum vector of this particle remains unchanged. This conclusion is called the law of conservation of angular momentum of particles.