Simple Application of Your First Mechanics Lesson

I’ve been trying to think of a simple application of the forces we’ve discussed in gymnastics.  Let’s apply our rules to a simplified muscle up.  Our athlete to the right starts from a hang and pulls / pushes himself up to a support (with the elbows straight and rings turned out of course).  We’re not going worry about a false grip, pull with bent elbows, flip over, or the dip push up.

Let’s start with a simple force diagram for a hang.  There is the force due to gravity and the athlete is exerting a force on the rings with his grip which is equal to the force due to gravity:

F(athlete) = F(gravity)

Let’s assume our athlete, let’s call him Bob, weighs 70 pounds.  So, in a still hang gravity is exerting 70 pounds of force.  Bob is creating a force upward amounting to 70 pounds.  In order for Bob to pull himself up he must exert more than 70 pounds of force upward.

As long as the athlete exerts more than 70 pounds of force upward, he will move upward.  When Bob reaches a support, he will again be exert 70 pounds of force, again upward, thus stopping his movement.

 F(athlete) > F(gravity)

Our Bob, being brilliantly coached, will hold his support for more than 2 seconds and hopefully lift up to a 2 second L support.  He will then reduce the force on the rings to less than 70 pounds and lower himself to an inverted hang.  Way to go Bob.

Your First Mechanics Lesson

Now that we’ve gotten through the definition of Force, we can start applying the physics to basic mechanics.

Way back when, when we were young and teachable, our first lesson in mechanics was the ‘block on and incline’.  When you place a block on an incline, three forces act on the block:  gravity, friction, and a normal force.

The basic question is when the block will begin to slide down the incline.  The block will begin to slide when gravity overcomes friction.

note: To simplify the equations, we first define the x-axis and the y-axis in accordance with the incline. (see diagram).

Next we look at the forces acting on the block:

Gravity:  As previously discussed (long ago), the force due to gravity is the weight of the object; the force acting on the block due to gravity.  This force acts directly downward.

Friction: Friction is the resistance to movement of a surface.  If you place your block on a rough surface, it less likely to slide than on a smooth surface.

Normal Force: A normal force is the resistance to gravity.  If you place your block on a table, it doesn’t fall into the table because the table applies a force to the block that equals the force due to gravity.

How does the block slide?

The block will slide when gravity overcomes friction.  In this case this means that the x-portion of the force due to gravity becomes larger than the x-portion of the force due to friction.

Notice that gravity acts on the block at an angle compared to the x and y axis. This means that part of the force acts in the x-axis and part in the y-axis.  The x portion of gravity balances the x portion of friction when the block doesn’t move.

The block’s potential to slide is base only in the x-axis so the normal force has no influence on the block’s sliding and can be ignored.  Only the x portion of gravity (gravity(x) in the diagram) and friction which acts only in the x-axis determine whether the block slides.

When the angle of the incline is sufficient to make gravity(x) exceed friction then the block will slide.

 

Is this it?

We’re nearing the end of basic physics.  Next we’ll apply the block on the incline principles to rotational movement …. Let’s face it, gymnastics isn’t about standing still, it’s about rotating.

Forces - Pushing and Pulling – Weight v. Mass

A force pushes or pulls a mass.  But, what exactly is a mass anyway?

Weight v. Mass

A force pushes or pulls a mass.  But, what exactly is a mass anyway?

Weigh yourself.  The scale tells you that you weigh 190 pounds (lbs).  After wondering how you got so heavy, a brilliant idea dawns on you.  You can lose weight by moving to Denver …  or if you’re already in Denver, try Bolivia, or … the Moon.

Mass is a constant measure of matter within an object.  Your mass remains constant wherever you go.

Weight is a measure of the force created on a mass by gravity.  This is why you lose weight by going to the Moon.

Force

Force is an attribute of physical action or movement measured by the ability of the attribute to move an object.

Force = Mass x Acceleration

F = ma

In the case of weight, this formula can be written as

Weight = Mass x Acceleration due to Gravity

W = mg

Be aware that our discussions from here on will apply use "mass" rather than "weight."

An Explanation of Acceleration

Can you accelerate without running faster?

Apparently you can.  This is why we started with distance v. displacement and moved on to speed v. velocity.  Acceleration is defined as the rate of change of velocity (not speed).

Linear Acceleration

Linear acceleration occurs as the athlete increases speed running down the vault runway (figure 7).

Figure 7

Between positions #1 and #2, the athlete increases his velocity (speed toward the vault table) from 0 ft/s to 4 ft/s.  At each position, he has again increased his velocity, reaching 12 ft/s before he reaches the vaulting board.

acceleration = change in velocity / time

a = Dv / Dt

This explains accelerating by increasing speed.  You can however, accelerate without increasing your speed.

Constant Acceleration

Figure 8

Go right back to the previous equation … Acceleration is a change in velocity and velocity has direction.  So, an athlete can run at a constant 5 ft/s and still accelerate.  Whenever an athlete changes direction, he is accelerating (figure 8).

Note the change in arrow direction for each position.  His change in displacement is not in a straight direction, but angular.  Thus his displacement, as a vector, is constantly changing.

Even though this athlete hasn’t changed his speed, he is constantly changing his direction, thus accelerating.  This is known as Constant Acceleration.

acceleration = change in velocity / time

a = Dv / Dt

 

These are the same equation.  They have a different result because v is a vector.

Changing Acceleration



Figure 9

But what happens if the athlete does increase his speed while running in circle?  This is called Angular Acceleration (figure 9).

This discussion is not yet ripe, so we’ll come back to angular acceleration later when we discuss rotation.

In the mean time, if your athlete starts demonstrating angular acceleration and cannot stop, I recommend using an elephant gun.

Power = Work over Time

Why, yes it does.  Not only does an athlete have to work very hard for a long time to develop the power necessary to be a great gymnast, but also in gymnastics physics, power does equal work over time.  So, the next time you try a line like “power equals work over time” and your athlete just laughs, flip some gymnastics physics on him and prove that you’re right.  

power = work / time

p = w / t

For now just remember the difference between speed and velocity.  We’ll start getting to this formula next time.  We’ll also start working on multiple universes and twisting moments.

The Difference between Speed and Velocity and why it Matters

Speed and velocity are the same thing aren’t they?  Even if they are technically different, it only mattered on your high school physics exam and not in the real world, right?

The Preliminaries --- Where’d that Kid Go?

 

D = “change in”

Figure 1



The first basic gymnastics physics formula isn’t even a formula, but it’s critical to understand the mechanics of the sport:

Start with an athlete standing in the middle of the floor exercise mat.  Then tell him to move 10 feet.  When he’s done, where is he?  With no more information than he moved a distance of 10 feet, you really can’t know.  You know he’s not more than 10 feet from where he started, but he could be anywhere within a circle with a radius of 10 feet (figure 1).

Distance is a measurement known as a “scaler”; a value with no direction.  In each case in figure 1, your athlete has moved 10 feet, but in no particular direction.

Displacement, on the other hand, has both size and direction.  Again, place your in the middle of the floor exercise mat, but this time have him move 10 feet east.  When he’s done, you’ll know exactly where he is.  He’s move from point 1 to point 2 (figure 2).


Figure 2

 This difference between distance and displacement will carry through all gymnastics physics.
 

The Difference Between Speed and Velocity

Speed and velocity carry over directly from distance and displacement.  Speed is the distance traveled over time elapsed.  Velocity is the change in displacement over time elapsed.

Speed

Locate an athlete at the beginning of the vaulting runway (figure 3, #1).  Then tell him to run at a speed of 12 feet (ft) per second (s).  After five seconds, where is the athlete?  You’d know he has run 60 feet and you might expect that after five seconds he is on the vaulting board.  But, you just don’t know ….

Speed is a scaler, again, a value with no direction.  So, your athlete may have run straight down the runway, but you didn’t tell him to do so.  He could have turned and run out the door and down to the park and still have met your instructions (figure 3, #2).

Figure 3

 

speed = distance / time

 

s = d / t

Velocity

Twenty minutes later, when you’ve finally located the kid, put him back at the end of the runway.  Then tell him to run at a speed of 12 feet (ft) per second (s) toward the vaulting table.  This time you know exactly where he is after five seconds; he’s on the vaulting board.  You know that because you gave him not just a speed to run at, but also a direction (figure 4, #2).

Figure 4

A value plus a direction is known as a “vector.”  Velocity requires a direction arrow in a diagram, but the formula can be written without the arrow:

 

velocity = change in position / time

 

v = Dx / Dt

Why the Difference Between Speed and Velocity Matters

Figure 5

Gymnastics technique is largely is governed, not only by how fast you can move, but in what direction you move.  An athlete who sets a backward salto on floor exercise can set it upward or backward or anywhere in between.  Merely evaluating the speed of the set in insufficient.  You (and he) need to know in what direction the salto is set (figure 5).A hard set backward is as much of a disaster as a soft set.  A hard set upward will give the athlete at least sufficient height.  A hard set backward will turn a layout into a whip-back.

FIgure 6

So, direction is critical.  Velocity is defined, not merely as movement over time, but as movement over time in a direction.



This is of course just a beginning, but a critical beginning.  If your athlete can move fast, but not in the right direction, if hardly matters.

Level 5 - Pommel Horse Stride Swing

There appears to be a misunderstanding of how the stride swings in the Level-5 pommel horse routine are to be performed. I’d like to at least clear up what I’m looking for as a judge. Let’s start with the requirements:

Requirements

First, each stride swing consists of a swing to the right and a swing to the left. See JO Manual pg 5.7. Both swings are evaluated.

Second, there are two requirements for a stride swing: Body position and amplitude. The required body position on pommel horse is straight body. The amplitude is no more than “on all pendular swings, false scissors and scissors, the top leg should be horizontal.” See JO Manual Chapter 3, Paragraph B(11)((b), pg 3.2. Regardless of popular opinion, the stated requirement for amplitude is not shoulder high, but horizontal.

Third, the basic technique for a pendular swing that will eventually lead to a shoulder high scissor or scissor handstand is a tap swing, much like the tap swing on parallel bars.

So, a stride s swing is required to be performed with a basically straight body and the leading leg at least horizontal on both the forward and backward sides of the swing.


How a stride swing is generally taught

For a stride swing to the right (right leg behind the horse, left leg in front).

1. Face forward (hips parallel to the horse).
2. Keeping both hands on the pommels, kick the right foot as high as possible.


How a stride should be taught

For a stride swing to the right (right leg behind the horse, left leg in front).

A tap swing should be taught: Arch the hips – relax through the bottom – drive the hips to the side, turning upward when fully extended. Until the tap swing can be accomplished, the athlete should swing straight body, driving his hips to the side.

A tap swing cannot be accomplished with the athlete hips aligned parallel to the horse; the torso simply does not bend that way. The athlete must turn his hips to align them closer to perpendicular to the horse.

For an athlete to swing with a straight body, the athlete must lean in the opposite direction of his swing (to the left on the forward swing, to the right on the backward swing). An athlete may need to push off his hands in order to lean sufficiently to keep his body straight. A great stride swing requires the athlete to push off his hands.

Note: Turning the hips will help to correct the nearly inevitable knee bend.

Most athletes have two or three deductions for each stride swing: Pike on forward swing, pike on the backward swing, and lack of extension throughout. Personally, I just take 0.1 for the average stride swing (plus the 0.1 for the knee bend).



Examples

Very Good: The first video shows a very good stride swing. His swing to the right is his better side, so this description references his second set of stride swings.

This athlete does not push of his hands, but still keeps his body basically straight. Note that the athlete does kick his foot high, but that is not what makes it a very good stride swing.

On the backward swing, the athlete’s left leg is at or near horizontal and his hips are touching his forearm. The front leg is higher than the back leg.

On the forward swing, the athlete’s right leg is very high, but the great part of this swing that his hip is touching his forearm and his torso and front leg remain in a basically straight body position.

This athlete could begin to push off his hands. Notice that he actually seems to be pulling with his right hand to hold onto the pommel.





Excellent: The second video shows excellent stride swings. Again, his swing to the right is his better side, so this description references his second set of stride swings.

This athlete does push of his right hand, keeping his body basically straight and swinging his hips much farther than the first athlete.

On the backward swing, the athlete’s left leg is at or near horizontal and his hips are touching his forearm. The front leg is higher than the back leg. This is one place where his swing could be even better. He could push of his left hand, but let’s give him a few years to get his scissor handstand :-).

On the forward swing, the athlete’s right leg is just above horizontal, meeting the requirement. The awesome part of this swing is that he is basically in a straight body position.





The athlete does not need to perform his stride swings exactly as shown in these videos, but this should give you the idea. I hope this helps.