Figure skating is an amazingly graceful sport when performed well by Olympic athletes. Skaters whirl and spin across the ice, effortlessly perform triple and quadruple jumps, and all the while are skating elegantly as if they are floating on the ice. As you watch these athletes skate during the Olympic Games (see video below), take a moment to think about the skills they are performing during their programs. The gold medalist for the women's singles competition will undoubtedly complete at least one quadruple jump during her performance. This means that she will take off from the ice, traveling at speeds approaching 20 mph, complete four revolutions in the air, and land lithely on one leg as she prepares for the next element. The skaters who medal in the Olympics will have jumps which leave the audience breathless. The jumps will appear to hang in the air, rotation speeds will make the skater a spinning blur, yet the take-offs and landings will be smooth and elegant. The jumps must be performed with an ease acquired only through years of hard work.

In the singles discipline of figure skating, performing complex jumps is an important aspect of each skater's program. Over the last ten years, the complexity of jumps performed by skaters has increased dramatically. For a skater to progress from a single, to a double, to a triple, and now even to a quadruple jump, he or she must either jump higher, rotate faster, or do some combination of the both. Typically as skaters progress from a single to triple jump, they jump higher and rotate faster in the air. The increase in jump height gives the skater more time to complete the required number of revolutions.

In addition to the minimal height and rotation speed requirements to complete the jumps, the skaters must also be concerned with their horizontal speed. It is important that a skater have enough speed to glide out of the jump into his or her next trick without a break in the fluidity of the program. Moreover, jumps performed at fast speeds with great heights and jump distances tend to leave a better impression with the judges, resulting in better marks for the skater.

Figure skating is a great example of physics in sports. Friction plays a huge role in ice skating. The most basic form of friction is portrayed in gliding across the ice. Ice skating is not actually skating on ice, but on a thin layer of water. The blade on the ice skating boot benefits of the property of ice that melts under pressure. Because temperature and pressure are inversely proportional, the lower the temperature, the more pressure is needed to melt ice. The sharp profile of the blade creates a high pressure on the ice, concentrating the whole weight of the skater on a small surface area; this facilitates the formation of a very thin liquid layer that reduces the friction. This allows the skater to glide on a layer of water between the blade and the ice. Thus a skater’s blade does not cut through ice, but melts through ice to allow a skater to skate.

In ice skating, friction is used to start a stroke. A stroke is a prime example of Newton's Third Law, which states: for every action, there is an equal and opposite reaction. As you angle your foot outward and extend the knee, the inside edge of the blade encounters the ice and the friction between the ice and the blade enables you to encounter resistance as you scrape the blade across the ice. You exert a force from edge into the ice. Friction enables the edge to grip into the ice. The equal and opposite force of the ice into the edge acts to propel the skater forward with kinetic energy.

Friction is also important in stopping. In order to stop properly, you apply pressure from your edge down into the ice. The continuous force from the edge down to the ice creates a drag which slowly removes the kinetic energy of skating across the ice converting it into heat and sound (that familiar scrape of the blades across the ice). The angular component of linear momentum is angular momentum. When an object rotates around a fixed axis, the force acting on the object is called the centripetal force. This force points inward, toward the center of the circle traced by the rotation. The velocity of the object points tangential to the circle traced.

Figure skaters spend a lot of time either spinning on the ice or rotating through the air. The faster a skater can spin, the more impressive that spin will be to the judges. Additionally, in the skater's short program, there is a minimal required number of revolutions a skater must complete in his or her spins. Studying the spin of an ice skater is an excellent way to demonstrate the physics of ice skating concept called angular momentum and how it is conserved. The skater moves slowly while arms spread across, when the skater brings her hands closer to her body, the speed of spinning increases so that the moment is maintained. To spin fast, or for a long time, the skater must develop a large amount of angular momentum. The speed of rotation during a skater's jump is also affected by his or her angular momentum. The ability of the skater to rotate faster in the air depends greatly on the skater’s angular momentum.

The angular component of linear momentum is angular momentum, where linear momentum equals mass times velocity p=mv. Momentum of inertia is basically a measure of the distribution of mass from the axis of rotation. Bigger mass or mass spread from the axis means bigger momentum of inertia. When an object rotates around a fixed axis, the force acting on the object is called the centripetal force. This force points inward, toward the center of the circle traced by the rotation. The velocity of the object points tangential to the circle traced. This is illustrated by swinging a ball on a string around your head. The vector for angular momentum points perpendicular to the velocity and force vectors. The moment of inertia depends on the mass of an object and also the distribution of that mass around the axis of rotation. So a skater can have a different moment of inertia based on whether their arms are extended or not. This can be compared to linear momentum where linear momentum equals mass times velocity. Angular momentum is conserved when no outside torques act on an object. As the moment of inertia decreases, the angular rotation has to increase to keep the same angular momentum. This is most evident when a figure skater spins. A skater that spins with arms outstretched has a large moment of inertia. As the skater brings the arms in closer to body (decreasing the moment of inertia), the rotational speed increases.

Once a skater has generated angular momentum, external forces may act to reduce the angular momentum of the skater. However, in situations, where there are no external forces producing torque about the axis of rotation, the skater's angular momentum will remain constant. This is called the conservation of angular momentum and holds true for any object.

While this concept is illustrated with a figure skating spin, angular momentum is not actually conserved in a spin due to the friction of the ice. In other words, even though a skater can increase and decrease his or her angular velocity by changing body position, as the spin progresses the skater's angular momentum decreases. Eventually, indifferent of the skater's body position, he or she will come to a stop. However, during jumps, when the skater is rotating in the air, his or her angular momentum is conserved. This means that however much angular momentum the skater generated during take-off (by applying forces to the ice), he or she can not change it in the air. This is a crucial concept for skaters to understand, because this means they need to generate enough angular momentum so that they will be able to complete their jumps. The skater can achieve a great rate of spin by storing angular momentum in arms and the push leg and then pulling those limbs in close to the body. This maneuver uses torque to generate angular momentum and then pulling the limbs close to the body reduces the moment of inertia. The rate of spin goes up to conserve angular momentum.

Two important conservation equations are:
1) angular momentum = (momentum of interia) x (rate of spin).
2) linear momentum = (mass) x (velocity).

Angular momentum is directly proportional to torque. The larger the torque, the greater the angular momentum. Torque is a force that causes rotation about an axis. In Latin, the word torque means to twist. The definition of torque is the product of the distance from the axis of rotation with the force that is perpendicular to the lever arm. Writing that as an equation, t = Fd. In skating, the most basic mechanism to create spin is to generate a torque
on his body by pushing against the ice. In edge spins, the skater pushes one foot against the ice to start the turn. You also see this in multiple rotation edge jumps. In these jumps, the skater takes off from the ice, turning the skate as he does so creating torque. Thus, the skater spins. The larger the force or the farther the force is from the axis of rotation, the larger the torque.

external image trplsalc.gifexternal image trplutz2.gif
Kinematics is also found in figure skating. The easiest way to start studying projectile motion is to study the path of a figure skater. Understanding the concept of projectile motion can help coaches and athletes most successfully master these complex athletic skills. A skater could jump straight up in the air, with absolutely no horizontal displacement - just a regular vertical jump on skates. However, this is not done in competition, skaters actually have vertical and horizontal displacement during theirs jumps. Furthermore, skaters are usually trying for the biggest jumps possible, high and covering a long distance.

When jumping for distance and height, the trajectory of the object is affected by the constant acceleration of gravity and air resistance. In sports such as speed skating and ski jumping, air resistance is critically important. Generally the faster an object is moving, the more important the influence of air resistance. In figure skating, the skater's generally are not moving fast enough for air resistance to affect their jumps.

Jumping in figure skating can be aided by changing linear momentum into vertical momentum in a manner similar to pole vaulting. The skater builds up a great speed (linear momentum) then the toe of a skate is pitched into the ice and the leg is used sort of like a pole in pole vaulting. Up to a point, the faster a skater moves going into a jump the higher and farther he/she will be able to leap.

Angular momentum can be carried into the jump by applying a torque just like when spinning and when the legs and arms are drawn into the body the skater spins in the air. To land with a smaller rate of spin the skater opens up his/her arms and the non-landing leg. A bad landing happens when the skater fails to control the angular momentum upon landing. If you notice almost all jumps result in landings that then proceed in a curved arc allowing the skater to gradually control some of the angular momentum gained in the leap.

With practice, a skater will acquire the skills to effectively use these forces to her advantage and that makes for impressive figure skating. Olympic skaters practice and practice to learn how to control momentum. Back in the 1980's triple jumps were considered the cutting edge of the sport. Now triple axels, triple toe loops, triple lutzes, and triple sal chows are common. In fact triple jump - double jump combinations are a required element. Many skaters do triple jump - triple jump combinations as their best move. Some of the most athletic skaters can even perform quadruple axels in practice with little effort. US skater Michael Weiss has landed a quadruple lutz in previous competitions and was a quarter revolution short on the jump in his Olympic performance. And a young Chinese skater was the first man to perform a quadruple jump-quadruple jump combination. It is not just the knowledge of physics of ice skating that helps figure skaters make exciting movements. Instead, it's the practice, the effort and fluid motion they put in with little or no regard for the theory.

But those of us who aren't so graceful will think of the physics instead.

Work Cite

Sonia Bansal - Is there any benefit to the sit spin? (Does the skater move faster than he would in an upright spin?)
Brandon Siegenfeld-What new technologies are being developed in skating/blade technology that would reduce friction on ice?
Robert Lopez - Is there a constant coefficient of friction for the blade on ice or does it depend on any other values?
Sam Edwards - Does the skater’s blade ever fail to melt the ice and cut it instead?
James Song- What is the difference between a salchow and a toe jump?
William Chan - How does the size of a skater affect physics of figure skating?
Kevin Norris - What safety measures are necessary (i.e. what if a skater hits a wall or falls at high velocity)?
Greg Sturm - How quickly does the thin layer of water solidify back into ice after the skater leaves it?
Sohini Sheth- Does the age/style/type of ice skate affect the skater's performance?
Douglas Chin - Wouldn't the landing during a backflip
embed the skate blades into the ice?
Naveen Shetty - Hockey players have a different cut on their blade..what is the advantage to the skaters' blade?