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# Mechanical Principles

The Rules of Sport Skill Technique
Mechanical principles of physics can be applied to sports. Using these rules as guides, athletes can achieve excellent technique to gain the greatest mechanical advantage. Newton's Laws of Motion are the foundation for these mechanical principles, which must be applied in concert with other training principles to achieve higher performance levels.

These mechanical principles of physics form a valuable guide for developing the optimum skating technique. However, there are many interpretations on how to apply the physics principles to a training program and effective teaching methods.

Principles from the Law of Inertia -
Newton's First Law states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force.
• Achieving skilled movements requires the effectively combination of linear and angular motion. For example, the hooking action of the edge/turn to convert the linear motion into an angular motion that establishes the spin's center.
• Two or more motions must be executed continuously in sequence. For example, in a jump the skater must spring into the air, complete the require number of revolutions, and check the rotation to achieve a controlled landing on the correct edge.
• There must be a balance of mass and/or velocity between partners and members of a synchro team. For example, each individual must alter their direction and force to stabilize their combined movements or centrifugal force will become uncontrollable.
• Control momentum efficiently for each body part to coordinate the entire body as a single unit. For example, changing positions from upright/layback to camel and/or sit spin positions.
Principles from the Law of Acceleration
Acceleration is a very important ability for a figure skater to possess.
• Acceleration/velocity is proportional to the force applied against the ice.  A skater who can increase his/her force applied to the ice increases their acceleration by an equal amount.
• The maximum acceleration is achieved when all body forces are coordinated to achieve thrust in either the forward or backward direction.  Body actions that do not contribute to the forward or backward motion should be minimized to prevent wasted energy and/or detract from productive creation of power.
• Lengthening the radius of our arms and/or free leg slows the body rotation; shortening the radius increases rotation. For example, a skater will achieve their maximum spinning rotation when they pull in their arms and free leg tight to the body. A came; spin can never approach the speed achieved in a scratch spin because the radius is longer in a camel spin.
• A skater establishes the path in the air at take off.  The axis of the core body may wobble or tilt on its axis. which can adversely affects the skater's ability to complete the rotation in a vertical position, and land the jump on one foot in a controlled position.
The Principles of Counterforce
A stable surface maximizes the potential counterforce that can be generated when force is applied against it. The less stable the surface, the less counterforce is generated. For example, a skidded edge does not produce the same spring force into the air for the skater as if a clean takeoff had been achieved.  The friction of the skid absorbs energy that is not transferred into the force that propels the skater into the air.
• To achieve maximum jumping height, it is necessary to push directly down upon take off. The direction of counterforce is directly opposite that of the applied force, and the applied force is most effective when it is perpendicular to the supporting surface because skidding the edge is minimized.
• Maximization of total force. The combination of thrusting from the jump foot and the free leg kick in the axel produce the total force into the air.

# The Biomechanics Behind Figure Skating

How does a figure skater jump so high, and spin so fast?

The Jump – Energy Conversion
There are several types of energy involved in a figure skating jump. The first type of energy comes from the muscles. In a jump, the skater pushes down on the ice, and thus the ice pushes an equal and opposite (upward) force on the skater. The skater then explodes up, converting mechanical potential energy through muscle power to kinetic energy.

As the skater sores higher, gravity slows him/her down, until the skater reaches a peak in which there is no more upward movement. Throughout this phase, kinetic energy is being converted into potential gravitational energy. As the skater falls, the potential energy gets converted back to kinetic energy, and the skater hits the ground with full kinetic energy (i.e. hard!).

The Spin – Angular Momentum
Figure skating would be pretty boring if the skaters did spins that us mere mortals could accomplish. So how do they spin in away that leaves us breathless?

It all rests in harnessing angular momentum. Angular momentum describes the rotational state of a spinning mass. Think of a stool that has a spinning seat. Once you get a push, you continue spinning at the same angular velocity (the speed at which you would be going if your spinning was converted to rolling down a street, for example) if no external forces act on you (note that you always come to a stop; this is indeed because of the external force of friction acting on the bearings, etc.).

If you are holding something heavy in both hands, you’ll notice that if you extend your arms outward during your spin, you will spin slower (but your moment of inertia will increase, thus keeping your angular momentum constant).

The essence of angular momentum can be described by the following equation:

```L = I*ω```

where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.

Angular momentum is always conserved. That is, during a spin, you will always have the same “L” value; thus, if you decrease I (moment of inertia), ω (angular velocity) will increase, and vice versa.

So, knowing that our moment of inertia is determined at the instant we lift off the ice, it is obvious that we want the largest moment of inertia to maximize the angular momentum during our spin. Then, according to the conservation of angular momentum, we can decrease our moment of inertia in the air, and thus increasing angular velocity, making us spin faster.

We accomplish this by spreading our arms wide and extending our free leg at the base of our jump. Then, during the spin, we bring our arms in close so that, since conservation of angular momentum holds (i.e. L is constant), as the moment of inertia decreases, our angular velocity increases, thus allowing us to execute more rotations.

An Example With Numbers
Let’s walk through a theoretical example. Refer to this page for common calculations of moments of inertia.

Assume a figure skater weighs 50kg (her torso is 40kg, her 2 arms and a leg are 10kg), her radius is 0.1m, her arm span is 0.6m and leg span is 1.0m.

We need to calculate the moment of inertia when her arms and free leg (her other leg is on the ground) are out (denoted Iout) and when they are pressed at her sides (denoted Iin). We will approximate her torso as a solid cylinder (whose moment of inertia is given by Itorso=mtorso*rtorso2). So, from the given information,

```Itorso = 1/2 * 40kg * (0.1m)2 =0.2 kg*m2```

Iin is comprised of Itorso and her 2 arms and a leg, which we can think of as 3 rods. They add 10kg of mass at a radius r from the cylinder (which in this case is 0.1m i.e. her radius). Assuming they are all of the same length (r distance away), their cumulative moment of inertia is given by mr2. So,

```Iin = Itorso + mr2 = 0.2 + (10kg * (0.1m)2) = 0.3 kg*m2```

When her leg and arms are out, they are further from the rotating body, so the moment of inertia will rise and the angular velocity will fall. Thinking of the arms and leg as rods, they have a moment of inertia as I=1/3*mr2 (see Wikipedia). So, let’s assume that of the 10kg each arm is 3kg and the leg 4kg. We can calculate the following:

```Iarm = 1/3 * 3kg * (0.6m)2 = 0.36 kg*m2```
`Ileg = 1/3 * 4kg * (1.0m)2 = 1.33 kg*m2`
```Iout = Itorso + 2*Iarm + Ileg = 0.2 + 2*0.36 + 1.33 = 2.25 kg*m2```

To finish it off, according to conservation of angular momentum,

```Lin = Lout So, Iin*ωin = Iout*ωout ωout/ωin = Iout/Iin = 2.25 / 0.3 = 7.5```

That means this skater is spinning 7.5 times faster when her arms and leg are tucked in than when they are extended outward. Holy!

Why has no one officially completed a quad axle?
A quad axle jump is 4.5 revolutions in the air. Assuming a jump time of 0.5s, a figure skater would need an average angular velocity of

```ω = 4.5rev / 0.5s = 9 rev/s```

to complete the jump. To grasp this speed, we can relate it to the RPM of a car. 9*60min = 540 rpm!! That’s about the same as a vehicle engine’s idling speed. On top of that, the skater has to control their landing so that it is elegant and fluid.

Remember that this is the average angular velocity; we will not be able to start this fast (with our leg and arms extended out), so we will be spinning even faster than that when our arms and leg are tucked in.

Good luck controlling a 540+ rpm jump and landing on the back outside edge of the opposite foot, backwards!
Source - wikipedia.org

References:

How to use Universal Laws & Principles To Your Advantage  A Universal Law or Principle is a general truth or rule that applies to all things anywhere they might be that is binding on anything that exist and are factors and parameters governing all creation.

Physics and Problem Solving  This lesson begins with a discussion of the law of inertia (a body at rest remains at rest and a body in uniform motion continues moving uniformly unless acted on by a net force). Next, the law of inertia is applied to a specific context, the use of seat belts and airbags in automobiles.

The Laws of Acceleration  Presented is a theory in fundamental theoretical physics that establishes the relationships between time, velocity, and the rate of acceleration for all material objects.  When properly formulated as given in this work, these relationships establish what appear to be two new natural laws of physics.  These laws, to be referred to as the Law of constant acceleration, and the Law of relative acceleration are in complete conformance with the principles of both, the time and energy theory, and the millennium theory of relativity.

Newton's Laws for Kids - 2nd Law   A Simple Explanation of Principles of Motion, Force, & Acceleration  Newton's first law tells us that a force is required to accelerate an object. Newton's second law answers the question about how much force is required.

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Resources:

The following internet links have been gleaned from personal communications
combined with information from public institutions and athletic organizations/
associations that have a web presence with information concerning team and
individual sports programs:

 Role of Physics in Skating Science of Dance

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