Figure Skating: Newsletter Challenge (10/11/05)

One of the major features of figure skating is the spin/twist, which is incorporated into a number of moves (e.g. the camel spin)

Skaters speed up and slow down during the execution of this move. To do this they extend and retract their arms - changing their angular inertia and therefore their spin speed, whilst conserving angular momentum

short explanation as late for meeting!!

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.

An extension to the original "figure skating" challenge by Roger Pink on the subject of angular momentum and its conservation: A short while after you spin a hard-boiled egg on a table top with the egg's longer axis parallel to the table-top (i.e. horizontal), the spinning egg stands up and continues spinning with its longer axis vertical to the table top. WHY? I don't know the answer. Is there anybody who does?

The answer, I believe, is simply friction.

Imagine an egg spinning on its side on a tabletop. Because of the curve of its shell, it is touching the table at only one point. However, the contact point is not fixed; it slides in a small circle around an imaginary vertical axis. As the egg slides, the friction created slows its rotation slightly, and the contact point with the table moves off-center. The egg begins to twist as it spins. One end slowly rises, until the egg stands vertically (but only for a few seconds). Note: this only holds true for a hard-boiled egg. If not hard-boiled, the fluid inside lags behind the shell - even though the shell is in motion, the fluid doesn't want to spin up.

As written in the 10/18 issue of Specs & Techs from GlobalSpec:

The simple answer is that is helps her to spin faster.

The detailed explanation is that objects executing motion around a point possess angular momentum. This is important because all experimental evidence indicates that angular momentum can be transferred, but it cannot be created or destroyed. In the 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. 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. This formula indicates one important physical consequence of angular momentum: because the 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 explicitly, this method of spin control is nothing but an invocation of the law of angular momentum conservation.)