Physics in Uneven Bars

Physics Sports Project

Uneven Bars

Centripetal Force

• The mass of the gymnast in kilograms multiplied by the linear velocity squared, divided by the radius (the gymnast’s height) is equal to the centripetal force.
• In the case of uneven bars, the centripetal force is caused by the gymnasts grip on the bar, and the bar itself is the point the gymnast is pulled towards. She holds the bar, causing her to revolve around the bar.
• When gymnasts want to transfer from one bar to another, they revolve around the bar several times, and then let go, breaking the centripetal force, and flying in the direction of the linear velocity at the time of release until they reach and grab the next bar, re-creating the centripetal force.

Angular Momentum

Angular momentum is equal to the product of mass, velocity and distance from mass to axis of rotation. When a gymnast first pushes off the mat, they have all the angular momentum they will get. From the time they push-off, no momentum is gained or lost. However, the gymnast is able to change the rate of their rotation in order to perform different moves without pushing off of anything. Therefore, they have to change their center of mass. For instance, if they pull their arms in, making their center of mass smaller, they will spin faster, and vice versa.

• The formula for angular momentum is the moment of inertia times the angular velocity

Friction

• Friction is the rubbing of one object or surface against another, or the force that resists motion between bodies in contact
• The formula for friction is the coefficient of friction times the two forces pushing the objects together
• Chalk actually increases friction between the bars and the gymnast's hand
• Chalk helps a gymnast’s hands glide smoothly over the bars, while at the same time providing enough friction for her hands to stick to the bar.

Acceleration

The gymnast’s centripetal acceleration is found by her velocity squared divided by her radius. Her radius is equal to her height if her legs are straight, but if she is in another position, such as a split, or bent in half with her legs by her head, then it is smaller. One of the reasons being short is an admirable quality in gymnasts is because it allows them to revolve faster.

When the gymnast wants to revolve faster, she separates her legs into a split, making her radius smaller, thus increasing her velocity. She does this so that she has enough velocity to jump to the other bar. She also needs to increase her speed from the mount, in order to perform tricks and overcome the force of gravity pulling down.

Bibliography

http://www.gymnasticsrevolution.com/Parents%2021.html

• http://www.topendsports.com/sport/gymnastics/physics.htm
• Foundations of Physics - Tom Hsu, Ph.D.
• http://gymnastics.isport.com/gymnastics-guides/explaining-the-uneven-bars-in-gymnastics/
• http://www.school-for-champions.com/science/friction_equation.htm

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