Viewed from any constant angle
, and velocity
, an isolated system
will not change how much it is spinning.
This raises the question, how does one define 'how much it is spinning'? The definition that Newton made is so: For any individual mass observed from a given frame of reference, the amount of 'angular momentum' is the product of the following three quantities:
- The object's mass
- The object's displacement vector from the center of the frame of reference (the origin), and
- The velocity of the object.
For those last two, use a cross product. This has the effect of eliminating all vector components of #3 which are not orthogonal to #2 (and vice versa). For the rest of us, that means that it only matters how much the object is moving to the side, not how much it's getting closer or further away. Also, it means that spin has a direction, along the axis of spin. Earth, for example, has rotational angular momentum pointing along its axis, in the direction pointing from the south pole to the north.
To get the angular momentum of a system larger than one mass, simply add up the angular momentum of each component object. Make sure you add them up using vector addition. To get the angular momentum of a continuous distribution of mass (any real object), you must take an integral.
Once you have determined the angular momentum of a system from a viewpoint, it will not change so long as it does not interact with anything else. That is the law of conservation of angular momentum.
Often, the dependence on where you look at it strikes one as odd. Does a car zipping by have angular momentum? Imagine that you stuck your hand out and let the car hit it. You would begin to spin as a result of the collision (among other less pleasant things). This is a hint (not proof) that it has angular momentum from your point of view.
Lastly, quantum mechanics includes a notion of 'spin' which is capable of absorbing angular momentum. This is not conventional since even point particles and particles without mass have spin. Nonetheless, the total amount of this newly redefined angular momentum does not change.