With the Winter Olympics coming up in a little over two weeks (the Opening Ceremonies are February 10), I thought it would be interesting to look into the physics of figure skating, one of the more popular sports at the Games (as long as there aren't any judging scandals!). In searching the web for documents on the physics of figure skating, I've noticed that they tend to focus on spinning and jumping. I will focus primarily on skaters' spinning motions, which implicate the physics concept of angular momentum.
Probably the easiest starting point is the concept of linear momentum, pertaining to an object traveling in a straight line. Momentum (symbolized by p) is defined as p = mv, or mass times velocity. The idea of a big running back in football running at a high speed would probably fit most people's lay conceptions of momentum, and more symbolically, one could say that a sports team or a political candidate has "momentum".
Angular momentum applies to an object rotating or spinning in circular motion about a central axis. Nebraska physicist Timothy Gay, in his book Football Physics (which I reviewed here), uses the example of opening or closing a door, such as the front door of a house. The door rotates in circular motion about an axis that is defined by the pins that go down through the hinges. A household door, of course, does not rotate all 360 degrees of a circle, but instead rotates more like a quarter of a circle (perhaps a revolving door would be a better example!).
Writes Gay:
We now define the angular momentum, L, of an object around some axis of rotation. It looks just like a linear momentum, p = mv, except that we replace the mass (m) with the moment of inertia (I), and the velocities (v) with angular velocities [Greek lowercase omega, which looks like a curvy w]. Thus L = Iw (p. 132).
A page earlier, he gives a concrete example of angular velocity:
If the door swings open a quarter of a full circle -- 90 degrees -- in one second, we would say that it has an "angular velocity," w, of 90 degrees per second. (Another unit of angular velocity you're more familiar with is "rpm," or revolutions per minute...)... The "moment of inertia," I, is the property of a body that tells us how hard it is to get it rotating for a given amount of torque. An important thing to remember about the moment of inertia is that it depends not only on the object's mass, but on how that mass is distributed. (pp. 131-132)
According to the Wikipedia, "...the greater the concentration of material away from the object's centroid, the larger the moment of inertia." In practice, however, moment of inertia appears to be fairly complicated to calculate, as there are different formulas according to the type of object in question.
At this point, we can envision different types of spinning objects for which we could calculate the angular momentum: doors slamming about their hinge axis, car wheels about their axles, old-fashioned vinyl records (33, 45, and 78 rpm) on a record player, spinners on board games, playground merry-go-rounds, and... figure skaters.
One figure skating phenomenon that's often noted is that, when a skater goes into a spinning motion, he or she appears to make faster revolutions when his or her arms are in close to the body than when the arms are outstretched. At Section H of this Central Michigan University document describes, barring the influence of any external torques (rotational forces), angular momentum must be conserved. In other words, angular momentum (moment of inertia times angular velocity) during one portion of the spinning routine must be equal to angular momentum during other portions.
According to an example in the Central Michigan document, if the skater spins with outstretched arms, the moment of inertia will be relatively large and the angular velocity relatively small. Bringing the arms in will reduce the moment of inertia, and the requirement of conserved angular momentum thus means that angular velocity must increase.
Spinning, of course, is not the only aspect of figure skating that implicates physics. Karen Knierman and Jane Rigby have compiled a page of topics and links related to the physics of ice skating, including skaters' jumps during their routines, what makes ice a skatable surface, and more on torque.
After studying the physics of figure skating a little bit, perhaps you'll have a new perspective as you watch the Olympics.