Gliding for Gold: The Physics of Winter Sports

4. Pucks and Rocks

4 PUCKS AND ROCKS Intrepid winter sports athletes hurl themselves at high speed over ice: they aim to slip, slide, slither, and glide their way from A to B in the fastest time, or at least faster than their opponents. Two of our winter sports, however, involve athletes hurling objects other than themselves. Sure, a hockey player is happy to turn himself into a projectile, directed at an opponent or at a location on the ice where he anticipates that the puck will be, but he will also send the puck across the ice or through the air. A curler sends a 40-pound granite rock over 100 feet along a sheet of ice, at a much more sedate pace. In this chapter we will investigate the unusual—indeed, decidedly odd—motion of ice hockey pucks and curling rocks. P U C K S A modern hockey puck is a short cylinder made of vulcanized rubber. It is a quite hard form of rubber but is not brittle; it deforms, instead of shattering, when struck. The cylinder has a diameter of three inches and is one inch thick. Pucks weigh about 6 ounces (170 g). A puck is a pretty mundane object to look at, but it attracts great excitement in a hockey fan by virtue of its position, when it flies at great speed towards his face or when it crosses a goal line. To a physicist, however, the humble puck is a very interesting object even when moving at low speeds. I will look at the physics of pucks at both extremes of speed, and begin with one that is sliding over the ice very slowly. 78 GLIDING FOR GOLD The Puck Stops Here A puck moving along the ice will, in general, be spinning about its center, as well as sliding. Spin is imparted by a hockey stick when the puck is struck, as we will see, and much of this angular speed is retained throughout the subsequent trajectory of the puck. Consider now a puck that rotates as it slides over the ice. The particular trajectory that I will consider here is one we don’t see all that often in hockey: the puck is allowed to come to a stop naturally, without interference from a player. The physics of puck motion is governed by sliding friction, with a friction coe≈cient of about 0.015. Theory predicts the following odd behavior: the puck stops moving over the ice at the same time as it stops spinning. It doesn’t matter how much speed or spin the puck starts out with—the two types of motion stop together. This prediction is borne out by experimental observation. It applies to any circular object sliding over the ice. The details di√er from one object to the next (depending mainly upon the sliding object’s mass distribution), but the result is the same: spinning and sliding cease simultaneously.1 This strange behavior was investigated a quarter century ago and is still generating interest in physics journals.2 It seems that the reason why spinning and sliding stop at the same time is because the two types of motion become tied together by the force of friction. The exact way in which they are connected depends upon the slider’s mass distribution, but it can be calculated. For a puck, for example, we know that as the sliding speed slows, spin rate slows down as the square root of speed. This means that during the time it takes the puck’s speed to drop to a quarter of its initial value, the spin will decrease to half its initial value. When the speed has been reduced to one-ninth, the spin will have been reduced to one-third. At the very end of the puck motion, just a fraction of a second before it stops, the spin and speed exhibit di√erent behavior; they are linked, but in 1. The same odd behavior may apply to sliding objects that are not circular, but I am not aware of any theoretical or experimental investigations into the sliding behavior of such shapes. By ‘‘mass distribution’’ I mean the variation of slider mass with radius. A puck has a uniform mass distribution—it is the same at all radii—whereas the mass distribution of a hemisphere sliding with the flat surface against the ice has a mass distribution that decreases with increasing radius. Such a hemisphere, even if it has the same...