How do Olympic figure skaters do triple axels and quadruple toe loops? It's all about angular momentum, vertical velocity, and conservation of angular momentum. NSF-funded sports scientist Deborah King, from the Department of Exercise and Sports Sciences at Ithaca College explains, using high-speed, high-resolution video of Olympic hopeful Rachael Flatt.
Figuring Out Figure Skating
LESTER HOLT, Anchor:
Every four years, we watch the stakes for Olympic figure skaters get higher, as they try to increase rotation in the air with their triple axels and quadruple toe loops. How do they do that? It’s a scientific principle that we asked Olympic hopeful Rachael Flatt and Deborah King, a sports scientist funded by the National Science Foundation, to help explain.
HOLT: Figure skaters make it look so easy: leaping off the ice…rotating through the air…and landing in a graceful arc. But make no mistake about it: figure skating is one of the most demanding of all the events at the Winter Olympics. For 17-year-old Rachael Flatt, the demands of training for the Olympics have to compete with other demands.
RACHAEL FLATT, U.S Figure Skating Team: I basically head to the rink at around six o'clock. I ice skate from six thirty to seven fifteen. And then, um, I go to school from seven thirty until about twelve thirty. And then, um, basically from there I go straight back to the rink.
HOLT: When she’s on the ice, this AP Physics student might want to consider the science that goes into her every jump. To see this science in detail, Rachael agreed to train in front of a special high-speed camera called the Phantom Cam. It has the astonishing ability to capture her jumps at rates of up to 1500 frames per second.
RACHAEL FLATT: It's very cool watching myself on the phantom camera. You get to see every phase of the jump. And it's pretty incredible just to be able to see every aspect of it, you know, where exactly the placement of your arm is, and where my head is, you know, uh, just everything is really cool.
HOLT: We brought the footage to Deb King, a Professor of Sports Science at Ithaca College, and an advisor to United States Figure Skating.
DR. DEBORAH KING, Ithaca College: A figure skating jump is a really complicated skill that combines a lot of different motions in it. They need to really optimize a lot of different conditions in terms of speed, force, vertical velocity, um, generating angular momentum, and put it all together in a package - with just the right timing - to execute the skill.
HOLT: Deb watched the Phantom Cam footage to explain what Rachael needs to get height and speed in one of her jumps. The first factor is Angular Momentum.
DEBORAH KING: In figure skating, angular momentum determines how fast you are going to be able to rotate in a jump in the air. So when you do a spin, if you generate more angular momentum, you have the potential to spin faster.
HOLT: Going into her jump, Rachael generates angular momentum by pushing off the ice with her foot. Pushing off the ice also generates Vertical Velocity, which will help get Rachael high enough to do her spins.
DEBORAH KING: The vertical velocity comes from producing forces from their jump during takeoff. This is sort of where action/reaction comes into play. As they contract their muscles and very powerfully extend their leg, they are pushing down against the ice. The ice will create a force up on them, which gives them vertical velocity. And it's pretty much the laws of accelerated motion, or projectile motion: that the more velocity you have at takeoff - and this is vertical velocity - the more she can keep going fast, straight up, the higher she'll jump.
HOLT: When Rachael spins on the ice, she exploits a law of physics to rotate faster and faster – almost as if by magic. How does she increase her speed while she’s spinning? The answer lies in her arms. When Rachael first starts to spin with her arms extended, she rotates slowly. But as she pulls her arms in closer and closer, she starts to rotate faster and faster. Rachel’s following an important law of physics – the “Law of Conservation of Angular Momentum.” You can’t go to jail for breaking this law. In fact, you can’t break it at all.
DEBORAH KING: As you get a smaller body position, your speed goes up. If you get a bigger body position, your speed goes down. So they react in opposite directions.
HOLT: Back in her office, Deb King spins on an office chair to make the same point.
DEBORAH KING: What I'm going to do is, when I'm spinning, I'm going to go from a very open position to a tight position. You'll see my speed change. So let's give that a try. [She spins around on chair.] So this is pretty fast. Slower. Fast. Slow. Fast. And I'm going to keep going, and the only way to stop is when I’m going to put my foot down and grab the table. I'm really dizzy right now. [Laughs]
HOLT: If Rachael can keep her body straight, and hold her limbs in close, she’ll achieve a higher rate of speed. But it’s not as easy as it looks.
RACHAEL FLATT: It's hard to stay as straight as possible. With every force, you know, you’re basically being pulled out everywhere, um, so it's easier to stay in when you're crossed, with your hands and your legs. It just makes the jump more efficient.
HOLT: But no matter how much attention she pays to the science of her jump, Rachael’s road to the Olympics will depend on her making skating look effortless.
RACHAEL FLATT: You never know what's going to happen. The unexpected is, you know, it's amazing. [Laughs]
Science Activity (Grades 6-9) from Lessonopoly
FIGURING OUT FIGURE SKATING
Objective: Use figure skating examples to demonstrate Newton’s Laws, projectile motion, and angular momentum.
Introduction notes for teacher:
This activity is intended for a class assignment after the viewing the NBC Learn FIGURING OUT FIGURE SKATING video clip. The activity presents physics concepts to explain figure skating and involves Newton’s Laws, projectile motion, and angular momentum. These topics are covered in most first-year physics classes. These are not, however, typical junior high topics.
One of the goals of figure skating is to maximize the number of turns in a single leap. This comes down to a matter of maximizing time in air and maximizing spin speed, both of which are determined by the direction and force of the skater’s push up off of the ice.
This activity will not try to teach the physics of projectiles or of angular momentum, but will attempt to give the student a “feel” for their meaning. The directions below are expressed as direction to the student. Each student should keep a log of results as suggested in each stop below.
Pt. One: Use Your Own Body (Keep a log of your results)
(1) Try to time yourself when jumping straight up to see how long you can stay up off of the ground. A classmate will have to help with the timing. Note which direction your feet are pushing on the floor.
(2) Now try to jump up and spin left at the same time. Repeat this jump several times and pay attention to how your feet a pushing on the floor.
(3) Repeat step 2, only spin to the right. Note how your feet a pushing differently.
Applying “physics” vocabulary:
(a) In step one, above, when you pushed down on the floor, you went up. This is an example of Newton’s Third Law, the law of equal and opposite reactions. Also in step one, when the floor pushed back on you, your body started moving upwards. This was an example of Newton’ First Law of Motion, which says that an unbalanced force causes objects to accelerate as long as the force is applied. (As long as you were in contact with the floor and able to push down on the floor.)
(b) In step two, when you spun your body to the left, your foot had to push towards the right. This also is an example of the Third Law, but it is also an example of “applying a torque” (More on this later.)
(c) In step three, when you spun your body to the right, your foot had to push towards the left. This is also an example of the Third Law, and it is also an example of “applying a torque”.
Pt. Two: Starting motion by using a swivel office chair: (Since jumping up and spinning at the same time is difficult, we will use an office chair to spin without the simultaneous jump that skaters must perform.)
(4) Sit on a swivel office chair with the chair back against your chest. You can then use the chair back for support. (There are also specially built physics spinning chairs for this demonstration.). Find a way to hold your legs so they cannot touch the floor or the base of the chair. Try to spin yourself. You should find this is impossible. You will do a lot of wiggling, but no spinning. (If you did spin, you were cheating somehow.)
(5) Reach sideways with one arm to push away from a wall or a heavy piece of furniture. Compare the direction of your push with the direction of your motion. Repeat this a few times. Compare the size of you push with your resulting speeds.
(6) Again, reach sideways with one arm, only this time, push sideways so that you start turning to the left. Note which direction you have to push in order to start to turn left. Repeat this so that you turn to the right.
Applying “physics” vocabulary:
(d) In step four, when you had nothing to push against, you had nothing to push back on you. This is another example of the Third Law of equal an opposite reaction. (No action, no reaction.)
(e) In step five, when you pushed on the wall, there was an opposite reaction against you that made you start moving away from the wall. Again, this is an example of the Third Law.
(f) In step six, when you pushed sideways against the wall, you started turning. This is another example of the Third Law. This sideways push is called a torque. Torques are required to start spinning motion, just like forces are required to cause linear motion.
Pt. Three: Changing motion of a spinning office chair: (In this part, have a fellow student give you a gentle spin while you arms are holding a pair of lightweight barbells. (You can use a pair of kilogram weights instead.) Hold them up against your sides.
(7) After the fellow student has given you a spin, and has stopped pushing you, see how long it takes (number of spins) to stop.
(8) Again, have a fellow student give you a spin. Once you are spinning, slowly extend your arms, with the barbells moving from your side to as far out as you can hold them. Make note of the change in your spin.
(9) Repeat step eight, above, only begin by holding the barbells out away from your body. Gradually pull the barbells in toward your body. Make a note of the change in your spin.
Applying “physics” vocabulary:
(g) In step seven, above, when your fellow student was giving you a spin he was applying a torque on you. Torques are necessary to give, or take away, spin. When he stopped, you coasted to a stop because of friction. The friction caused a torque in the opposite direction. This opposite torque took away your spin. When you have a spin, the physicist says you have angular momentum. Angular momentum changes only when a torque is applied. When the applied torque is in the same direction as your spin, you spin faster. We say your angular momentum increases. When the torque is against your spin, like the friction torque, you go slower. We say your angular momentum decreases.
(h) In step 8, above, you slowed your spin a lot faster than if you simply slowed because of friction. In fact, even if there were no friction, you would still have slowed down when you extended your arms outwards. This slowdown is caused by an effect called “Conservation of Angular Momentum”.
(i) In step 9, above, your spin rate increased, because your arms came closer to your center, in spite of the friction which should have caused a slowing of the spin. This increased spin rate is also caused by an effect called “Conservation of Angular Momentum”.
(j) Angular momentum is one of several quantities that are “conserved” in special circumstances. An explanation of this concept is beyond the scope of this activity. Briefly, the student should understand that angular momentum depends on two measurements: an object’s spin rate and the object’s distance from the spin center (a radius).
The figure skating competition has grabbed headlines at the 2018 Winter Olympics in South Korea.
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