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Mechanical PrinciplesThe Rules of Sport Skill TechniqueMechanical 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. 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.
Acceleration is a very important ability for a figure skater to possess.
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.
The Biomechanics Behind Figure SkatingHow does a figure skater jump so high, and spin so fast? The Jump – Energy ConversionThere 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 MomentumFigure 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:
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 NumbersLet’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 I_{out}) and when they are pressed at her sides (denoted I_{in}). We will approximate her torso as a solid cylinder (whose moment of inertia is given by I_{torso}=m_{torso}*r_{torso}^{2}). So, from the given information,
I_{in} is comprised of I_{torso} 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 mr^{2}. So,
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*mr^{2} (see Wikipedia). So, let’s assume that of the 10kg each arm is 3kg and the leg 4kg. We can calculate the following: I_{arm}
= 1/3 *
3kg
* (0.6m)^{2} = 0.36 kg*m^{2} I_{leg} = 1/3 * 4kg * (1.0m)^{2} = 1.33 kg*m^{2} I_{out} = I_{torso} + 2*I_{arm} + I_{leg}
= 0.2 + 2*0.36 + 1.33 = 2.25 kg*m^{2} To finish it off, according to conservation of angular momentum,
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
Recommended Reading: 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. Skill Development Environment: Mental Training: 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:
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