The Conservation of Angular Momentum

In a closed system angular momentum is constant. This conservation law mathematically follows from continuous directional symmetry of space (no direction in space is any different from any other direction).

THE CAT FALLING PROBLEM

The falling cat problem consists of explaining the underlying physics behind the common observation of the cat righting reflex: how a free-falling cat can turn itself right-side-up as it falls, no matter which way up it was initially, without violating the law of conservation of angular momentum.
Although somewhat amusing, and trivial to pose, the solution of the problem is not as straightforward as its statement would suggest. The apparent contradiction with the law of conservation of angular momentum is resolved because the cat is not a rigid body, but instead is permitted to change its shape during the fall. The behavior of the cat is thus typical of the mechanics of deformable bodies.
The solution of the problem, originally due to (Kane & Scher 1969), models the cat as a pair of cylinders (the front and back halves of the cat) capable of changing their relative orientations. Montgomery (1993) later described the Kane--Scher model in terms of a connection in the configuration space that encapsulates the relative motions of the two parts of the cat permitted by the physics. Framed in this way, the dynamics of the falling cat problem is a prototypical example of a nonholonomic system (Batterman 2003), the study of which is among the central preoccupations of control theory. A solution of the falling cat problem is a curve in the configuration space that is horizontal with respect to the connection (that is, it is admissible by the physics) with prescribed initial and final configurations. Finding an optimal solution is an example of optimal motion planning (Arbyan & Tsai 1998; Xin-sheng & Li-qun 2007).
In the language of physics, Mongomery's connection is a certain Yang-Mills field on the configuration space, and is a special case of a more general approach to the dynamics of rigid bodies as represented by gauge fields (Montgomery 1993; Batterman 2003).


MORE ON THE CONSERVATION OF ANGULAR MOMENTUM

If a planet is found to rotate slower than expected, then astronomers suspect that the planet is accompanied by a satellite, because the total angular momentum is shared between the planet and its satellite in order to be conserved.
The conservation of angular momentum is used extensively in analyzing what is called central force motion. If the net force on some body is directed always toward some fixed point, the center, then there is no torque on the body with respect to the center, and so the angular momentum of the body about the center is constant. Constant angular momentum is extremely useful when dealing with the orbits of planets and satellites, and also when analyzing the Bohr model of the atom.
The conservation of angular momentum explains the angular acceleration of an ice skater as she brings her arms and legs close to the vertical axis of rotation. By bringing part of mass of her body closer to the axis she decreases her body's moment of inertia. Because angular momentum is constant in the absence of external torques, the angular velocity (rotational speed) of the skater has to increase.
The same phenomenon results in extremely fast spin of compact stars (like white dwarfs, neutron stars and black holes) when they are formed out of much larger and slower rotating stars (indeed, decreasing the size of object 104 times results in increase of its angular velocity by the factor 108).
The conservation of angular momentum in Earth--Moon system results in the transfer of angular momentum from Earth to Moon (due to tidal torque the Moon exerts on the Earth). This in turn results in the slowing down of the rotation rate of Earth (at about 42 nsec/day), and in gradual increase of the radius of Moon's orbit (at ~4.5 cm/year rate). [from the Wiki]

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[laughproductions47Xx]

so in short is it the sum of momentum that ic conserved not the spin because i think thats wrong is it?

[veritaszeitgeist]

@laughproductions47Xx kind of. my explanation is not fully formed. i just wanted to drop cats. both axes rotate independently so they cancel each other out, and the net effect is zero, so momentum is conserved.

[REDace2]

I appreciate that the cats were compensated for their trauma.

[MaxPlank91]

Nice..