A system's total angular momentum remains constant if the net external torque acting on the system is zero. Examples of such systems include a freely spinning bicycle tire that slows over time due to torque arising from friction, or the slowing of Earth's rotation over millions of years due to frictional forces exerted on tidal deformations. However in the absence of a net external torque, the angular momentum remains conserved. The conservation of angular momentum principle requires a change in angular velocity if the moment of inertia of the rotating system changes.
There are several examples of objects that obey the principle of conservation of angular momentum. Tornadoes are one example. Storm systems that create tornadoes rotate slowly. When the radius of rotation decreases, angular velocity increases, sometimes to the furious level of a tornado. The solar system is another example of how the conservation of angular momentum works in the universe. The solar system was created from a huge cloud of gas and dust that initially had rotational energy. Gravitational forces caused the cloud to contract, and the rotational rate increased due to the conservation of angular momentum.
In the case of human motion, one would not expect angular momentum to be conserved when a body interacts with the environment as its foot pushes off the ground. Astronauts floating in space aboard the International Space Station have no angular momentum relative to the inside of the ship if they are motionless. Their bodies continue to have this zero value no matter how they twist about as long as they do not push themselves off the side of the vessel.
This text is adapted from Openstax, College Physics, Section 10.5: Angular Momentum and its Conservation and Openstax, University Physics Volume 1, Section 11.3: Conservation of Angular Momentum.
