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Transcript
Physics in Gymnastics Rachel Lewis Some Background Forces Energy Physics in Gymnastics Momentum Rotational Motion Rachel Lewis Mercyhurst University April 2014 Overview Physics in Gymnastics Rachel Lewis Some Background Forces Energy Momentum Rotational Motion This presentation will reveal ways in which physics and mathematics can be seen in sports, specifically vaulting in gymnastics It can be very beneficial to athletes to understand these connections in order to improve their technique. I hope that this will provide a possible answer the age old question that echos throughout classrooms: ”When will I ever use this in the real world?” Some Background Springboard Horse Runway Vaulting Physics in Gymnastics Rachel Lewis Some Background Forces I Vaulting is a component of both men’s and women’s gymnastics competition. Energy Momentum Rotational Motion Vaulting Physics in Gymnastics Rachel Lewis Some Background Forces I I Vaulting is a component of both men’s and women’s gymnastics competition. Gymnasts run with maximum speed toward the vault and then drive their legs into a springboard. The springboard launches the gymnast towards the vault. Energy Momentum Rotational Motion Vaulting Physics in Gymnastics Rachel Lewis Some Background Forces I Vaulting is a component of both men’s and women’s gymnastics competition. I Gymnasts run with maximum speed toward the vault and then drive their legs into a springboard. The springboard launches the gymnast towards the vault. I As the gymnasts hands are positioned on top of the vault, they push off and perform a series of recognized vault maneuvers. Energy Momentum Rotational Motion Vaulting Physics in Gymnastics Rachel Lewis Some Background Forces I Vaulting is a component of both men’s and women’s gymnastics competition. I Gymnasts run with maximum speed toward the vault and then drive their legs into a springboard. The springboard launches the gymnast towards the vault. I As the gymnasts hands are positioned on top of the vault, they push off and perform a series of recognized vault maneuvers. I Most vaults include a form of handstand, somersault, and twisting motion. Energy Momentum Rotational Motion The Yurchencko Vault Physics in Gymnastics Rachel Lewis Some Background Forces Energy Every Olympic gold medalist in vault since 1988 has performed a Yurchencko vault. Momentum Rotational Motion The Yurchencko Vault Physics in Gymnastics Rachel Lewis Some Background Forces Energy Every Olympic gold medalist in vault since 1988 has performed a Yurchencko vault. I A Yurchencko vault consists of performing a round-off before reaching the springboard. Momentum Rotational Motion The Yurchencko Vault Physics in Gymnastics Rachel Lewis Some Background Forces Energy Every Olympic gold medalist in vault since 1988 has performed a Yurchencko vault. I A Yurchencko vault consists of performing a round-off before reaching the springboard. I In a Yurchencko vault gymnasts have FOUR opportunities to push off of a surface. This will be important later! Momentum Rotational Motion Forces Crushed It! Newton’s First Law Physics in Gymnastics Rachel Lewis Some Background Newton’s first law states that objects in motion will stay in motion unless acted upon by an outside force. Forces Energy Momentum Rotational Motion Newton’s First Law Physics in Gymnastics Rachel Lewis Some Background Newton’s first law states that objects in motion will stay in motion unless acted upon by an outside force. I So, gymnasts running toward the vault will stay in motion until an outside force acts on them. Forces Energy Momentum Rotational Motion Newton’s First Law Physics in Gymnastics Rachel Lewis Some Background Newton’s first law states that objects in motion will stay in motion unless acted upon by an outside force. I So, gymnasts running toward the vault will stay in motion until an outside force acts on them. AND Forces Energy Momentum Rotational Motion Newton’s First Law Physics in Gymnastics Rachel Lewis Some Background Newton’s first law states that objects in motion will stay in motion unless acted upon by an outside force. I So, gymnasts running toward the vault will stay in motion until an outside force acts on them. AND I After the vault, gymnasts will stay in the air until an outside force acts on them. Forces Energy Momentum Rotational Motion Newton’s First Law Physics in Gymnastics Rachel Lewis Some Background Newton’s first law states that objects in motion will stay in motion unless acted upon by an outside force. I So, gymnasts running toward the vault will stay in motion until an outside force acts on them. AND I After the vault, gymnasts will stay in the air until an outside force acts on them. This force is Gravity! Forces Energy Momentum Rotational Motion Newton’s Second Law Physics in Gymnastics Rachel Lewis Some Background Forces Newton’s second law is: F = (m)(a) Energy Momentum Rotational Motion Newton’s Second Law Physics in Gymnastics Rachel Lewis Some Background Forces Newton’s second law is: F = (m)(a) Energy Momentum I This tells us that mass and acceleration are directly proportional in regards to force. Rotational Motion Newton’s Second Law Physics in Gymnastics Rachel Lewis Some Background Forces Newton’s second law is: F = (m)(a) Energy Momentum I I This tells us that mass and acceleration are directly proportional in regards to force. Thus, the more mass and acceleration a gymnast has when running at the vault, the greater the force produced on the vault. Rotational Motion Newton’s Second Law Physics in Gymnastics Rachel Lewis Some Background Forces Newton’s second law is: F = (m)(a) Energy Momentum I I I This tells us that mass and acceleration are directly proportional in regards to force. Thus, the more mass and acceleration a gymnast has when running at the vault, the greater the force produced on the vault. Gymnast must reach a maximum velocity on their approach to the springboard in order to produce a maximum force! Rotational Motion Newton’s Third Law Physics in Gymnastics Rachel Lewis Some Background Forces Newton’s third law states that for every action, there is an equal but opposite reaction. This is represented by force pairs. Energy Momentum Rotational Motion Newton’s Third Law Physics in Gymnastics Rachel Lewis Some Background Forces Newton’s third law states that for every action, there is an equal but opposite reaction. This is represented by force pairs. I When a gymnast jumps on a springboard, she exerts a force on the springboard, which in turn gives an equal force to the gymnast and propels her into the air. Energy Momentum Rotational Motion Newton’s Third Law Physics in Gymnastics Rachel Lewis Some Background Forces Newton’s third law states that for every action, there is an equal but opposite reaction. This is represented by force pairs. I I When a gymnast jumps on a springboard, she exerts a force on the springboard, which in turn gives an equal force to the gymnast and propels her into the air. When the gymnast pushes off the horse, her hands exert a downward force and have an equal upward force exerted on them by the horse. Energy Momentum Rotational Motion Energy Ok. Do NOT trip! Energy and Vaulting Physics in Gymnastics Rachel Lewis Some Background I Gymnasts gain kinetic energy, which is the energy of motion, when running towards the springboard. Forces Energy Momentum Rotational Motion Energy and Vaulting Physics in Gymnastics Rachel Lewis Some Background I I Gymnasts gain kinetic energy, which is the energy of motion, when running towards the springboard. When the gymnast jumps on the springboard she has only potential spring energy. Forces Energy Momentum Rotational Motion Energy and Vaulting Physics in Gymnastics Rachel Lewis Some Background I I I Gymnasts gain kinetic energy, which is the energy of motion, when running towards the springboard. When the gymnast jumps on the springboard she has only potential spring energy. The potential spring energy is then transformed to kinetic and gravitational potential energy as the gymnast pushes off the springboard. Forces Energy Momentum Rotational Motion Energy and Vaulting Physics in Gymnastics Rachel Lewis Some Background I I I I Gymnasts gain kinetic energy, which is the energy of motion, when running towards the springboard. When the gymnast jumps on the springboard she has only potential spring energy. The potential spring energy is then transformed to kinetic and gravitational potential energy as the gymnast pushes off the springboard. As the gymnast flips through the air, her kinetic energy increases as her potential gravitational energy decreases. No energy is lost or gained, it is CONSERVED. Forces Energy Momentum Rotational Motion Max gravitational potential Max spring potential Momentum Momentum and Vaulting Physics in Gymnastics Rachel Lewis Some Background Forces Energy Momentum Rotational Motion I The angle at which the gymnast hits the springboard is very important!. Momentum and Vaulting Physics in Gymnastics Rachel Lewis Some Background Forces Energy Momentum Rotational Motion I The angle at which the gymnast hits the springboard is very important!. I A more vertical angle produces a greater force to propel the gymnast higher into the air. Conservation of Momentum Physics in Gymnastics Rachel Lewis Some Background Forces Energy I Due to conservation of momentum, gymnasts cannot gain any angular momentum once they have sprung off the horse. Momentum Rotational Motion Conservation of Momentum Physics in Gymnastics Rachel Lewis Some Background Forces Energy I Due to conservation of momentum, gymnasts cannot gain any angular momentum once they have sprung off the horse. I Greater angular momentum means the gymnast has more potential for flips. Momentum Rotational Motion Conservation of Momentum Physics in Gymnastics Rachel Lewis Some Background Forces Energy I Due to conservation of momentum, gymnasts cannot gain any angular momentum once they have sprung off the horse. I Greater angular momentum means the gymnast has more potential for flips. I Gymnast gain angular momentum by pushing off from a surface at an angle. Momentum Rotational Motion Yurchenko Vault Physics in Gymnastics Rachel Lewis Some Background Forces Energy Momentum I Recall: In a Yurchenko vault gymnasts have FOUR opportunities to gain angular momentum from pushing off of a surface. Rotational Motion Yurchenko Vault Physics in Gymnastics Rachel Lewis Some Background Forces Energy Momentum I Recall: In a Yurchenko vault gymnasts have FOUR opportunities to gain angular momentum from pushing off of a surface. I This increases the downwards momentum when landing on the springboard and horse, in turn increasing the upwards momentum when pushing off. Rotational Motion Yurchenko Vault in Slow Motion 4! 2! 3! 1! Angular Momentum Physics in Gymnastics Rachel Lewis Some Background Forces Energy Momentum I Angular momentum is represented by the formula L = (r )(m)(v ) Rotational Motion Angular Momentum Physics in Gymnastics Rachel Lewis Some Background Forces Energy Momentum I Angular momentum is represented by the formula L = (r )(m)(v ) I Since angular momentum and the mass of the gymnast are constants, lowering the r (the distance of the body from the axis of rotation) will lead to an increase in velocity . Rotational Motion Angular Momentum Physics in Gymnastics Rachel Lewis Some Background Forces Energy Momentum I Gymnasts often curl into a tight ball in midair to achieve more flips because the smaller the r, the faster they spin. Rotational Motion Angular Momentum Physics in Gymnastics Rachel Lewis Some Background Forces Energy Momentum I Gymnasts often curl into a tight ball in midair to achieve more flips because the smaller the r, the faster they spin. I Extending their body slows the rotational speed, ensuring the gymnast land smoothly on her feet. Rotational Motion Example of Tucking squeeze! Rotational Motion Just keep spinning, Just keep spinning! Rotational Motion and Vaulting Physics in Gymnastics Rachel Lewis Some Background Forces Energy Momentum Rotational Motion I We know when gymnasts leave the mat, the angular momentum from their push off is all they will get, none can be gained or lost! Rotational Motion and Vaulting Physics in Gymnastics Rachel Lewis Some Background Forces Energy Momentum Rotational Motion I We know when gymnasts leave the mat, the angular momentum from their push off is all they will get, none can be gained or lost! I However, for various moves, gymnasts need to change their rate of rotation in the air... Changing Rotational Velocity Physics in Gymnastics Rachel Lewis Some Background Forces Energy I More air time allows more time to rotate and increased rotational velocity makes the time required to complete each move shorter. Momentum Rotational Motion Changing Rotational Velocity Physics in Gymnastics Rachel Lewis Some Background Forces Energy I I More air time allows more time to rotate and increased rotational velocity makes the time required to complete each move shorter. Gymnasts change their rate of rotation in the air by changing the distance of their center of mass from their axis of rotation.(Just like we saw in angular momentum!) Momentum Rotational Motion Changing Rotational Velocity Physics in Gymnastics Rachel Lewis Some Background Forces Energy I More air time allows more time to rotate and increased rotational velocity makes the time required to complete each move shorter. I Gymnasts change their rate of rotation in the air by changing the distance of their center of mass from their axis of rotation.(Just like we saw in angular momentum!) I Many of these concepts are very similar and go hand in hand Momentum Rotational Motion Physics in Gymnastics The End! Rachel Lewis Z 0 ∞ sinx dx x x 2 + ex y= 2 x − ex Some Background Forces Energy Momentum THE END! YAY! Questions? Comments? Concerns? lim 1 2 f (x) = √ e (x−π) 2π ln(1 + e 3x ) x→∞ x Z xt dt 1 + xt 1 2 f (x) = √ e (x−π) 2π Rotational Motion
