Starting with this article, George Hery will be offering his expertise on the biomechanics of gymnastics.Â George has put his engineering studies at Iowa to work throughout his gymnastics/trampoline career, designing equipment, enhancing safety features and educating gymnasts and coaches.Â We are pleased that George will be sharing his knowledge with GymSmarts.Â The first article will help to define physics with a emphasis on gymnastics, the following articles will deal with Movement, Initiation, Control, Efficiency; Parabolas; and Twisting.Â Â
This first article will cover the basic principles; later articles will explore practical application of this powerful science.Â Â Â Â Â Â Â Â Â Â Â Our movements are governed by “the laws of physics,” which are, for most people, quite baffling even though we have been obeying them for thousands of years.
Â Â Â Â Â Â Â Â Â Â Â Our sport of gymnastics is made up of many different movements; some are quite simple, but many are very complex. Knowledge and understanding of these “laws of physics” is necessary if you want to be an excellent teacher, instructor or coach.
Â Â Â Â Â Â Â Â Â Â Â I will attempt, with this article, to present these difficult concepts so that everyone can learn and understand “George’s Laws of Movement”.
We will explore three types of movements.
1. Linear movement - is movement in a straight line. Not many gymnastics movements in this category.
2. Angular or rotational movement - involves rotation around an axis or axes.
3. Parabolic flight - whenever a body flies through the air, the flight path or trajectory of the center of gravity of that body is a parabola; a smooth symmetrical curve mathematically (graphically) represented as (ay = bx squared + c). This will be covered in detail in a future article.
We must also learn the necessary terminology and understand the basic concepts, which are presented below.
Center of Gravity - (c.g.) that one point where all of the mass of a body may be considered to be concentrated. (for purposes of calculation)
For our human body when in a straight body position the c.g. is in the trunk region near the waist. Understand though that our c.g. changes position when we change positions; raising our arms raises the c.g., if we pike or arch the c.g. may be completely outside of our body.Â
Mass - (m) the quantity of matter; the density of a body multiplied be its volume.
Weight - (w) the attractive (or gravitational) force that the earth exerts on a body. (w = mg)
Inertia - the resistance to change in motion. Bodies at rest tend to remain at rest and bodies in motion tend to remain in motion unless acted upon by outside forces. From this it is easy to see that heavier bodies will have more inertia. We should also note that forces do not always produce a change in motion. Consider a small boy who tries to lift a 400-pound weight, but can only apply 200 pounds of lifting force; the weight would not move.
GEORGE’S FIRST LAW OF MOVEMENT
Â Â Â Â Â Â Â Â A force or combination of forces is required in order to initiate, change or stop movement.
Â Â Â Â Â Â Â Â Forces - pushes, pulls and resistances. There are external forces such as the force of gravity, contact with another object, collisions, friction forces, wind resistance, etc. There are also internal forces such as muscular contractions, coefficients of restitution (the ability of an object to return to its original shape after it has been deformed) in high bar rails, uneven bar rails, parallel bar rails, vault boards, trampoline springs, etc.
Â Â Â Â Â Â Â Â Force through the center of gravity - a force or combination of forces directed through the center of gravity of a body in free space produces only linear movement for that body.
Â Â Â Â Â Â Â Â Eccentric forces - forces not directed through the center of gravity produce angular movement (rotation) around an axis; this axis is called the axis of rotation.
Â Â Â Â Â Â Â Â Axis of Rotation - that point or line about which a body rotates. In free space the axis of rotation is the center of gravity, during a giant swing the axis of rotation is the bar, during the takeoff from the vault board the axis of rotation is the feet of the vaulter, etc. etc.
Â Â Â Â Â Â Â Â A Couple - equal but oppositely directed forces equally distanced from the center ofÂ gravity of an object also produces angular (rotational) movement.
Â Â Â Â Â Â Â Â Resultant force - the magnitude and direction of movement for the center of gravity of a body being acted upon by more than one force.
Speed - how fast a body is moving.
Momentum - mass x velocity. A speeding bullet has great momentum because of its tremendous velocity even though its mass is small; a train moving at only 3 miles per hour also has great momentum because of its tremendous mass.
GEORGE’S SECOND LAWÂ Â OF MOVEMENT
Â Â Â Â Â Â Â Â A body in motion has momentum and that momentum will be conserved (remain constant) unless outside forces act upon the body.
Â Â Â Â Â Â Â Â Radius of rotation - (r) the distance from the axis of rotation to the c.g. of each element of mass of the body that is rotating. For calculation purposes we assume that the gymnast’s body is one element of mass located at the c.g. if the gymnast is rotating around a bar. During a straight body back flip there would be two radii of rotation; one for the upper body and another for the lower body.
Â Â Â Â Â Â Â Â Moment of Inertia - (MI) the resistance to change in angular (rotational) movement. It is found by multiplying each element of mass in a body by the square of its radius of rotation (r) and then adding all of these products for the entire body. For simplification (calculation) purposes use the c.g. of each segment of the body that is rotating; then (MI = m x r squared). Understand that there can be “Moments of Inertia” for different parts or segments of a body. Because the mass of a body remains constant, the moment of inertia will change as the radius of rotation changes.
Â Â Â Â Â Â Â Â Angular Momentum - (H) the moment of inertia multiplied by the angular velocity. (H = m x r squared x V) This is a very important concept to understand as it is used to initiate and control all angular movement. Because (H) remains constant and (m) remains constant, we can greatly change (V) by changing (r), and even more so because (r) is squared. This means that by going from a straight body at the start of a double back flip to a tucked body as you approach the top of the parabolic flight path, you will greatly increase your angular velocity. In actual practice, you will spin about 5 times faster in the tuck than you were spinning when you started with a straight body. Much more on angular momentum in future articles.
GEORGE’S THIRD LAW OF MOVEMENT
Â Â Â Â Â Â Â Â For every action there is an equal and opposite reaction.Â Â Â Â
Â If we push on a wall, the wall pushes back on us; if we push downward on the floor, the floor pushes upward on us; if we push downward hard enough, the floor will push upward hard enough to make us go up in the air. We call that a jump. If we are in free space and turn our upper body and arms to the right, our legs and lower body will react by turning to the left; if we throw our head and arms forward and downward, our legs move upward into a pike jump. Understand these concepts!!!
Â Â Â Â Â Â Â Â Transfer of momentum - There are times when the momentum from a segment of our body can be transferred to the entire body and this action may give a great advantage toward accomplishing a movement or skill. Try this experiment. While standing with straight legs and arms at your sides, swing the arms up really vigorously and sharply stop them just as they are straight out in front of you. You should experience a lifting of your entire body and if you do this vigorously enough you may even come off the ground without jumping. We use this transfer of momentum concept in many gymnastics skills; an example would be a cast to handstand on the uneven bars or high bar. Try to figure out the forces involved and where the transfer of momentum comes in.
Â Â Â Â Â Â Â Â Â Â Â Now really try to get a grasp of these basic concepts and we will begin our practical application of “the laws of movement” with the next article. For now, practice perfection.
About George HeryGeorge H. Hery has led a fascinating life as an acclaimed gymnast, acrobat, performer, and mentor. He is a true acrobatic legend - in 2004 he was inducted into the World Acrobatic Society’s Hall of Legends. He has traveled the world for shows, competitions, stunt performances, and for the pure sake of exploration. His accomplishments have been recognized by numerous organizations and governments.