Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Physics in Gymnastics

Rachel Lewis

Mercyhurst University

April 2014

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Overview

This presentation will reveal ways in which physics andmathematics can be seen in sports, specifically vaulting in

gymnastics It can be very beneficial to athletes tounderstand these connections in order to improve their

technique. I hope that this will provide a possible answer theage old question that echos throughout classrooms: ”When

will I ever use this in the real world?”

Some Background

Springboard

Horse

Runway

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Vaulting

I Vaulting is a component of both men’s and women’sgymnastics competition.

I Gymnasts run with maximum speed toward the vaultand then drive their legs into a springboard. Thespringboard launches the gymnast towards the vault.

I As the gymnasts hands are positioned on top of thevault, they push off and perform a series of recognizedvault maneuvers.

I Most vaults include a form of handstand, somersault,and twisting motion.

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Vaulting

I Vaulting is a component of both men’s and women’sgymnastics competition.

I Gymnasts run with maximum speed toward the vaultand then drive their legs into a springboard. Thespringboard launches the gymnast towards the vault.

I As the gymnasts hands are positioned on top of thevault, they push off and perform a series of recognizedvault maneuvers.

I Most vaults include a form of handstand, somersault,and twisting motion.

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Vaulting

I Vaulting is a component of both men’s and women’sgymnastics competition.

I Gymnasts run with maximum speed toward the vaultand then drive their legs into a springboard. Thespringboard launches the gymnast towards the vault.

I As the gymnasts hands are positioned on top of thevault, they push off and perform a series of recognizedvault maneuvers.

I Most vaults include a form of handstand, somersault,and twisting motion.

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Vaulting

I Vaulting is a component of both men’s and women’sgymnastics competition.

I Gymnasts run with maximum speed toward the vaultand then drive their legs into a springboard. Thespringboard launches the gymnast towards the vault.

I As the gymnasts hands are positioned on top of thevault, they push off and perform a series of recognizedvault maneuvers.

I Most vaults include a form of handstand, somersault,and twisting motion.

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

The Yurchencko Vault

Every Olympic gold medalist in vault since 1988 hasperformed a Yurchencko vault.

I A Yurchencko vault consists of performing a round-offbefore reaching the springboard.

I In a Yurchencko vault gymnasts have FOURopportunities to push off of a surface. This will beimportant later!

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

The Yurchencko Vault

Every Olympic gold medalist in vault since 1988 hasperformed a Yurchencko vault.

I A Yurchencko vault consists of performing a round-offbefore reaching the springboard.

I In a Yurchencko vault gymnasts have FOURopportunities to push off of a surface. This will beimportant later!

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

The Yurchencko Vault

Every Olympic gold medalist in vault since 1988 hasperformed a Yurchencko vault.

I A Yurchencko vault consists of performing a round-offbefore reaching the springboard.

I In a Yurchencko vault gymnasts have FOURopportunities to push off of a surface. This will beimportant later!

Forces

Crushed It!

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Newton’s First Law

Newton’s first law states that objects in motion willstay in motion unless acted upon by an outside force.

I So, gymnasts running toward the vault will stay inmotion until an outside force acts on them.

AND

I After the vault, gymnasts will stay in the air until anoutside force acts on them.

This force is Gravity!

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Newton’s First Law

Newton’s first law states that objects in motion willstay in motion unless acted upon by an outside force.

I So, gymnasts running toward the vault will stay inmotion until an outside force acts on them.

AND

I After the vault, gymnasts will stay in the air until anoutside force acts on them.

This force is Gravity!

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Newton’s First Law

Newton’s first law states that objects in motion willstay in motion unless acted upon by an outside force.

I So, gymnasts running toward the vault will stay inmotion until an outside force acts on them.

AND

I After the vault, gymnasts will stay in the air until anoutside force acts on them.

This force is Gravity!

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Newton’s First Law

Newton’s first law states that objects in motion willstay in motion unless acted upon by an outside force.

I So, gymnasts running toward the vault will stay inmotion until an outside force acts on them.

AND

I After the vault, gymnasts will stay in the air until anoutside force acts on them.

This force is Gravity!

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Newton’s First Law

Newton’s first law states that objects in motion willstay in motion unless acted upon by an outside force.

I So, gymnasts running toward the vault will stay inmotion until an outside force acts on them.

AND

I After the vault, gymnasts will stay in the air until anoutside force acts on them.

This force is Gravity!

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Newton’s Second Law

Newton’s second law is: F = (m)(a)

I This tells us that mass and acceleration are directlyproportional in regards to force.

I Thus, the more mass and acceleration a gymnasthas when running at the vault, the greater the forceproduced on the vault.

I Gymnast must reach a maximum velocity on theirapproach to the springboard in order to produce amaximum force!

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Newton’s Second Law

Newton’s second law is: F = (m)(a)

I This tells us that mass and acceleration are directlyproportional in regards to force.

I Thus, the more mass and acceleration a gymnasthas when running at the vault, the greater the forceproduced on the vault.

I Gymnast must reach a maximum velocity on theirapproach to the springboard in order to produce amaximum force!

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Newton’s Second Law

Newton’s second law is: F = (m)(a)

I This tells us that mass and acceleration are directlyproportional in regards to force.

I Thus, the more mass and acceleration a gymnasthas when running at the vault, the greater the forceproduced on the vault.

I Gymnast must reach a maximum velocity on theirapproach to the springboard in order to produce amaximum force!

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Newton’s Second Law

Newton’s second law is: F = (m)(a)

I This tells us that mass and acceleration are directlyproportional in regards to force.

I Thus, the more mass and acceleration a gymnasthas when running at the vault, the greater the forceproduced on the vault.

I Gymnast must reach a maximum velocity on theirapproach to the springboard in order to produce amaximum force!

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Newton’s Third Law

Newton’s third law states that for every action, there isan equal but opposite reaction. This is represented byforce pairs.

I When a gymnast jumps on a springboard, sheexerts a force on the springboard, which in turngives an equal force to the gymnast and propels herinto the air.

I When the gymnast pushes off the horse, herhands exert a downward force and have an equalupward force exerted on them by the horse.

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Newton’s Third Law

Newton’s third law states that for every action, there isan equal but opposite reaction. This is represented byforce pairs.

I When a gymnast jumps on a springboard, sheexerts a force on the springboard, which in turngives an equal force to the gymnast and propels herinto the air.

I When the gymnast pushes off the horse, herhands exert a downward force and have an equalupward force exerted on them by the horse.

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Newton’s Third Law

Newton’s third law states that for every action, there isan equal but opposite reaction. This is represented byforce pairs.

I When a gymnast jumps on a springboard, sheexerts a force on the springboard, which in turngives an equal force to the gymnast and propels herinto the air.

I When the gymnast pushes off the horse, herhands exert a downward force and have an equalupward force exerted on them by the horse.

EnergyOk. Do NOT trip!

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Energy and Vaulting

I Gymnasts gain kinetic energy, which is theenergy of motion, when running towards thespringboard.

I When the gymnast jumps on the springboard shehas only potential spring energy.

I The potential spring energy is then transformed tokinetic and gravitational potential energy as thegymnast pushes off the springboard.

I As the gymnast flips through the air, her kineticenergy increases as her potential gravitationalenergy decreases. No energy is lost or gained, it isCONSERVED.

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Energy and Vaulting

I Gymnasts gain kinetic energy, which is theenergy of motion, when running towards thespringboard.

I When the gymnast jumps on the springboard shehas only potential spring energy.

I The potential spring energy is then transformed tokinetic and gravitational potential energy as thegymnast pushes off the springboard.

I As the gymnast flips through the air, her kineticenergy increases as her potential gravitationalenergy decreases. No energy is lost or gained, it isCONSERVED.

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Energy and Vaulting

I Gymnasts gain kinetic energy, which is theenergy of motion, when running towards thespringboard.

I When the gymnast jumps on the springboard shehas only potential spring energy.

I The potential spring energy is then transformed tokinetic and gravitational potential energy as thegymnast pushes off the springboard.

I As the gymnast flips through the air, her kineticenergy increases as her potential gravitationalenergy decreases. No energy is lost or gained, it isCONSERVED.

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Energy and Vaulting

I Gymnasts gain kinetic energy, which is theenergy of motion, when running towards thespringboard.

I When the gymnast jumps on the springboard shehas only potential spring energy.

I The potential spring energy is then transformed tokinetic and gravitational potential energy as thegymnast pushes off the springboard.

I As the gymnast flips through the air, her kineticenergy increases as her potential gravitationalenergy decreases. No energy is lost or gained, it isCONSERVED.

Max spring potential

Max gravitational potential

Momentum

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Momentum and Vaulting

I The angle at which the gymnast hits the springboardis very important!.

I A more vertical angle produces a greater force topropel the gymnast higher into the air.

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Momentum and Vaulting

I The angle at which the gymnast hits the springboardis very important!.

I A more vertical angle produces a greater force topropel the gymnast higher into the air.

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Conservation of Momentum

I Due to conservation of momentum, gymnastscannot gain any angular momentum once they havesprung off the horse.

I Greater angular momentum means the gymnast hasmore potential for flips.

I Gymnast gain angular momentum by pushing off from asurface at an angle.

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Conservation of Momentum

I Due to conservation of momentum, gymnastscannot gain any angular momentum once they havesprung off the horse.

I Greater angular momentum means the gymnast hasmore potential for flips.

I Gymnast gain angular momentum by pushing off from asurface at an angle.

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Conservation of Momentum

I Due to conservation of momentum, gymnastscannot gain any angular momentum once they havesprung off the horse.

I Greater angular momentum means the gymnast hasmore potential for flips.

I Gymnast gain angular momentum by pushing off from asurface at an angle.

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Yurchenko Vault

I Recall: In a Yurchenko vault gymnasts have FOURopportunities to gain angular momentum from pushingoff of a surface.

I This increases the downwards momentum when landingon the springboard and horse, in turn increasing theupwards momentum when pushing off.

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Yurchenko Vault

I Recall: In a Yurchenko vault gymnasts have FOURopportunities to gain angular momentum from pushingoff of a surface.

I This increases the downwards momentum when landingon the springboard and horse, in turn increasing theupwards momentum when pushing off.

Yurchenko Vault in Slow Motion

1!2!

3!

4!

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Angular Momentum

I Angular momentum is represented by the formula

L = (r)(m)(v)

I Since angular momentum and the mass of the gymnastare constants, lowering the r (the distance of the bodyfrom the axis of rotation) will lead to an increase invelocity .

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Angular Momentum

I Angular momentum is represented by the formula

L = (r)(m)(v)

I Since angular momentum and the mass of the gymnastare constants, lowering the r (the distance of the bodyfrom the axis of rotation) will lead to an increase invelocity .

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Angular Momentum

I Gymnasts often curl into a tight ball in midair toachieve more flips because the smaller the r, the fasterthey spin.

I Extending their body slows the rotational speed,ensuring the gymnast land smoothly on her feet.

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Angular Momentum

I Gymnasts often curl into a tight ball in midair toachieve more flips because the smaller the r, the fasterthey spin.

I Extending their body slows the rotational speed,ensuring the gymnast land smoothly on her feet.

Example of Tucking

squeeze!

Rotational Motion

Just keep spinning,Just keep spinning!

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Rotational Motion and Vaulting

I We know when gymnasts leave the mat, the angularmomentum from their push off is all they will get, nonecan be gained or lost!

I However, for various moves, gymnasts need to changetheir rate of rotation in the air...

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Rotational Motion and Vaulting

I We know when gymnasts leave the mat, the angularmomentum from their push off is all they will get, nonecan be gained or lost!

I However, for various moves, gymnasts need to changetheir rate of rotation in the air...

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Changing Rotational Velocity

I More air time allows more time to rotate and increasedrotational velocity makes the time required to completeeach move shorter.

I Gymnasts change their rate of rotation in the air bychanging the distance of their center of mass from theiraxis of rotation.(Just like we saw in angularmomentum!)

I Many of these concepts are very similar and go hand inhand

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Changing Rotational Velocity

I More air time allows more time to rotate and increasedrotational velocity makes the time required to completeeach move shorter.

I Gymnasts change their rate of rotation in the air bychanging the distance of their center of mass from theiraxis of rotation.(Just like we saw in angularmomentum!)

I Many of these concepts are very similar and go hand inhand

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

Changing Rotational Velocity

I More air time allows more time to rotate and increasedrotational velocity makes the time required to completeeach move shorter.

I Gymnasts change their rate of rotation in the air bychanging the distance of their center of mass from theiraxis of rotation.(Just like we saw in angularmomentum!)

I Many of these concepts are very similar and go hand inhand

Physics inGymnastics

Rachel Lewis

Some Background

Forces

Energy

Momentum

Rotational Motion

The End!

THE END! YAY!Questions?Comments?Concerns?

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1 + x tdt

f (x) =1√2π

e(x−π)2

limx→∞

ln(1 + e3x)

x

f (x) =1√2π

e(x−π)2

∫ ∞0

sinx

xdx

y =x2 + ex

x2 − ex