# Conservation of Angular Momentum: Application

JoVE Core
Physik
Zum Anzeigen dieser Inhalte ist ein JoVE-Abonnement erforderlich.  Melden Sie sich an oder starten Sie Ihre kostenlose Testversion.
JoVE Core Physik
Conservation of Angular Momentum: Application

### Nächstes Video11.13: Gyroscope

For any object rotating about a rotational axis, the conservation of angular momentum holds if no external torque acts on it.

For example, suppose the Sun, having an angular velocity of two point six times ten to the power of negative six radians-per-second, collapses into a white dwarf such that its radius decreases by a factor of five hundred. Assuming that the lost mass carries away no angular momentum, what will be the white dwarf's final rotational kinetic energy?

Here the known quantities are initial and final radii, initial and final masses, and the angular velocity of the Sun. The unknown quantity is the final rotational kinetic energy of the white dwarf.

Here, the conservation of angular momentum holds, and assuming that the Sun and the white dwarf each have uniform spherical densities, substituting for their moment of inertia, the final angular velocity of the white dwarf can be calculated.

The rotational kinetic energy of the white dwarf can be calculated by substituting the value of the final angular velocity.

## Conservation of Angular Momentum: Application

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.