In gymnastics, gymnasts learn to manipulate their bodies in order to take advantage of Newton’s Laws of Motion so that they can pull off spectacular tricks. So, how do they do it?
The event we will look at today is the vault. In the vault, a competitor tries to execute as many flips, twists, and spins as possible, whilst maintaining good execution and a balanced landing, after jumping off a springboard and over the horse, as shown below.
In order to complete as many flips and spins in the air, two things are important: air time, and rotational velocity. More air time allows more time to rotate, and increased rotational velocity makes the time required to complete each manoeuvre shorter.
The inevitable force that will end the jump is, of course, gravity. Gravity is a downwards force, so in order to delay hitting the ground and the jump ending, the gymnast has to exert an upwards force.
Now, let’s just think about what force is. A force is any influence that changes the motion of a body. So any force that is applied, must affect the velocity (to some degree) of the body it is acting on. Isaac Newton came up with a formula that represented this, known as Newton’s Second Law.
Where F is the force, m is the mass of the body it is acting upon, and a is the acceleration of the body it is acting on.
In other words, the force is directly proportional to the acceleration it will cause. It is important to note that the technical definition of acceleration is not the same as the colloquial one. Technically, acceleration is a change in velocity, not speed. Therefore, an object can accelerate without getting any faster or slower, just by changing direction! By running around in a circle you are actually constantly accelerating.
The first force that the gymnast produces is in their run up, when they are trying to reach a maximum velocity before reaching the springboard. They then jump onto the springboard, and are launched into the air. Why does this happen?
This is due to Newton’s Third Law of motion. This states that all actions have an equal and opposite reaction. People utilise this all the time, for example when jumping. When we jump, we exert a force upon the ground beneath our feet, which gives us an equal force and propels us into the air. However it is not just us that moves, the Earth accelerates as well! However, since Newton’s First Law means that mass is inversely proportional to acceleration, the Earth’s huge mass means that we accelerate 75 billion billion times faster than the Earth, rendering this negligible in everyday situations.
Back to gymnastics: When the gymnast jumps onto the springboard, they exert a downward force, causing the spring to compress. The spring then returns to its original shape and exerts an equal, upward force on the gymnast. This is the same principle behind trampolines, and all elastic materials.
The gymnast then pushes off the horse using their hands, again exerting a downwards force and having an equal upward force exerted to them by the horse.
So, how can a gymnast increase the downward forces upon the springboard and the horse? One obvious answer is to run faster in the run up. A higher velocity means a higher momentum, which allows the gymnast to exert a greater downward force upon the springboard, which launches them further into the air. This then increases their downward momentum when landing on the horse, meaning there will be an even greater upward force.
But there is another method of increasing the upward force, which is to adjust the angle at which you land on the springboard. When running, you having a very high forward momentum, some of which you convert to upwards momentum after landing on the board, as in the diagram below.
Not much of the sideways momentum (as we look at it on the diagram) is converted into upwards momentum. However, if the gymnast hit the springboard at a more vertical angle, then the resultant force would propel them further into the air.
But how would a gymnast manage to come from this more vertical angle?
A Russian gymnast named Natalia Yurchenko came up with the answer in the 1980’s, now known as the “Yurchenko vault”. By doing what is known as a ‘round-off’ before reaching the spring, essentially two consecutive half-flips, she greatly increased the downwards momentum when landing on the springboard, and therefore the upwards momentum when springing off. Here is a video of Beth Tweddle demonstrating this technique.
The Yurchenko has another advantage; it provides an extra chance for the gymnast to increase their angular momentum. Angular momentum is defined as the product of the body’s mass, linear velocity, and distance from the axis of rotation. This can be shown in the following formula:
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