Conservation of Angular
Momentum


Our theory for the origin of the Solar System is a very old one with some modern innovations called the Nebular Hypothesis. A crucial ingredient in the nebular hypothesis is the conservation of angular momentum.

Angular Momentum

Objects executing motion around a point possess a quantity called angular momentum. This is an important physical quantity because all experimental evidence indicates that angular momentum is rigorously conserved in our Universe: it can be transferred, but it cannot be created or destroyed. For the simple case of a small mass executing uniform circular motion around a much larger mass (so that we can neglect the effect of the center of mass) the amount of angular momentum takes a simple form. As the adjacent figure illustrates the magnitude of the angular momentum in this case is L = mvr, where L is the angular momentum, m is the mass of the small object, v is the magnitude of its velocity, and r is the separation between the objects.

Ice Skaters and Angular Momentum

This formula indicates one important physical consequence of angular momentum: because the above formula can be rearranged to give v = L/(mr) and L is a constant for an isolated system, the velocity v and the separation r are inversely correlated. Thus, conservation of angular momentum demands that a decrease in the separation r be accompanied by an increase in the velocity v, and vice versa. This important concept carries over to more complicated systems: generally, for rotating bodies, if their radii decrease they must spin faster in order to conserve angular momentum. This concept is familiar intuitively to the ice skater who spins faster when the arms are drawn in, and slower when the arms are extended; although most ice skaters don't think about it explictly, this method of spin control is nothing but an invocation of the law of angular momentum conservation.


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