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Science of sports

Physics and sports are connected. Understanding the physics of motion is helpful to athletes and sports persons to perform well. It is also helpful in training them, designing better equipment and preventing injuries. Force, rotational motion, moment of inertia, angular momentum, work and energy are some of the concepts useful in understanding physics of sports.

In Olympics, more than 10,000 athletes from more than 200 countries participate after undergoing highly focused and rigorous physical as well as psychological training. It is important to understand science behind the highly demanding performance.

Rotational motion, Angular momentum and Moment of Inertia

Some of examples for angular momentum and rotational motion are:
Diving, Ballet pirouette, Ice skater balancing, Ski turns, Bicycle or motorcycle riding, Football pass or lateral spinning, Spinning top, Frisbee, Spinning gyroscopes for orbital orientation, Helicopter, Earth rotation for daily constancy and seasons, Baseball curve pitch, Baseball outfield throw with backspin for longer distance, Tennis topspin to keep ball down, Golf ball dimpling and backspin for range.


Diving

Diving is one of the most popular events in the Olympics and it is a very good example of physics in action. When divers leaps off the board and reaches the apex of their jump, they carry with them an angular momentum that remains constant throughout the entire fall. The divers push off the platform in a way that provides torque to cause angular momentum which gives them rotational motion.

Inertia is an object’s resistance to changes in its state of motion. Moment of inertia is the torque required to change the angular velocity. When divers jump off the diving board, they need to carry with them a specific amount of torque that will allow them to rotate in the air. Torque won’t change during the fall, so its value is defined right from the initial leap.

A diver who is leaping off the platform must do so in such a way that he or she jumps into the air already possessing enough torque that will translate into an adequate amount of rotational motion. This rotational motion will result in enough angular momentum that the diver can use to spin fast enough to pull off enough tricks in the short time between jump and landing.

Angular momentum is conserved when no external torque acts on it. Thus when the moment of inertia decreases angular velocity increases. The angular momentum will remain the same while the diver is falling. But what the diver can change is his or her moment of inertia. The diver can reduce the time required for diving to less than 2 seconds, say in to a 10 meter dive, she needs to change the moment of inertia by pulling the legs and arms closer to the point of rotation. The moment of inertia decreases and the angular velocity increases. When she enters water, she increases the moment of inertia again to decrease the angular speed. Stretching the limbs out will increase the moment of inertia, thereby decreasing the angular velocity, which is essential for a neat and flawless dive into the water.

The magnitude of momentum is the product of an object’s mass and velocity. Angular momentum is just like linear momentum except that it deals with rotational motion. Angular momentum also depends upon: the angular velocity and the moment of inertia.
L = Iω
where L represents angular momentum, I represents moment of inertia and ω represents the rotational speed in units of radians per second.
The angular velocity is a measure of how fast the object is spinning. The angular momentum remains constant during the dive and angular velocity increases as the moment of inertia decreases. The moment of inertia depends not only on the mass but also on the location of the mass relative to the point of rotation. The farther the mass is from the rotation point, the greater the moment of inertia. So the diver increases the speed by reducing momentum of inertia by pulling legs and arms closer to the point of rotation.

Skating

Angular momentum is the product of the moment of inertia (the product of the mass of the object and the square of its perpendicular distance from the axis of rotation) and rotational velocity. If we look at a skater who turns on the tip of her skates, she draws her arms and a leg inward, which reduces the distance between the axis of rotation and some of her mass, thereby reducing the moment of inertia and her friction with the air. Since angular momentum is conserved, rotational velocity increases. Friction represents the force resisting the displacement of one surface over another and it is a braking force that needs to be overcome to move forward. In skating, the melted liquid layer in-between ice and skate has macroscopic thickness due to the heat generated by friction.

Swimming

Swimmers suffer the gravity and the force of water in swimming. Swimmers need to reduce the area occupied by their body as it moves through the water so that by reducing the area, they reduce resistance (friction), which acts as opposing force in the water. So, position of the swimmer’s body and movement of their arms are very important to swim faster and in conserving energy.

Pole vaulting

In pole vaulting, athletes transform chemical energy into kinetic energy of their body while running. Some part of this kinetic energy becomes elastic potential energy (deformation of the pole) and the remaining energy becomes gravitational potential energy, which again is transformed into kinetic energy while the athletes freely fall away from the bar.


Cycling

Aerodynamics describes the ability of an object to overcome air resistance and plays an important role in cycling races. In cycling, the bicycle composition and design, the clothing worn by the cyclist, the positioning of the rider on the bicycle surface and cycling closely behind another in a zone of reduced air pressure (drafting) helps them to be more efficient by consuming less energy. The shorter is the distance between cyclists, the larger is the decrease in wind resistance and hence cyclists save energy by drafting. Drafting is used to reduce wind resistance and it is seen in cycling, running, swimming and car racing as well. Computational Fluid Dynamics (CFD) is a computational technique used to model drafting that can help athletes to prepare and train more efficiently.

American Football

Passing, blocking, running, tackling, kicking in American football illustrate several concepts in physics such as inertia, momentum, Newton's laws of motion, projectile motion and kinematics. Tackling and blocking runners relies on three important principles of physics, namely Impulse, Conservation of momentum and Rotational motion.

Impulse is the product of the applied force and the time over which that force is applied. If a defensive back wants to tackle a running back, he could use less force to stop him by increasing the time in contact with the running back. The motion of ball carrier and tackler after collision depends on momentum of the ball carrier and the tackler. It also depends on whether tackler holds on to the ball carrier after collision. The total momentum of those involved remains the same before and after the collision. Depending on the momentum of ball carrier and tackler, they stop at the point of contact (equal momentum), ball carrier breaks the tackler (momentum of ball carrier is more) and moves on or the ball carrier may be knocked down (ball carrier has less momentum).

Players tackle a runner low so that the runner's feet will be rotated in the air in the direction of the tackle. All bodies will rotate easiest about their centre of mass. This rotational force is called torque, and is the product of the amount of force applied and the distance from the centre of mass at which the force applied. Because torque is a product, the same torque can be applied to an object at different distances from the centre of mass by changing the amount of force applied. So less force is required farther out from the centre of mass than closer in. So, by tackling a runner low, far from the centre of mass, it takes less force to tackle him than if he were tackled high. A lineman crouches low so that his centre of mass is closer to the ground. This makes it hard for an opposing player to move him as he will not rotate.

Soccer

"Bend it like Beckham" is a famous saying about the way David Beckham spins the ball in his famous free kicks. The intuitive kick of Beckham has the effect that the Magnus force and the Bernoulli’s principle will have on his strike, as they explain how a ball swerves when spin is put on it. If ball is kicked hard enough the airflow over the surface will become turbulent and the drag force which slows its flight will remain low allowing the ball to travel very fast. Then, when it slows a little and the airflow becomes laminar, any spin on the ball will cause it to swerve according to Bernoulli’s principle and the Magnus force.

The trick is to hit it with just the right amount of power and spin so that the turbulent flight lasts until the ball passes the defenders in the wall and at the same time the ball slows down into laminar flow, where the ball will curve most before the goal keeper gets to it and it is difficult to block balls struck with sidespin.

Baseball

The reaction time for a batter is only a fraction of a second. It may take about 0.1 second for the hitter just to locate the ball and during this time ball must have travelled about 12 feet. The batter then takes about seven hundredths of a second to calculate speed, spin and trajectory by which time ball has already travelled another 10 feet. It then takes the batter 0.017 second for the brain and body to work together to execute a swing. This means that the batter has about 0.09 second to make the decision whether to swing or not. If the hitter hesitates for even a thousandth of a second, it could result in a foul ball or a strike.

The laws of motion that apply to hitting the ball are Newton's second law which says that the acceleration of an object is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object. It also depends on the angle at which bat hits the ball. The faster the pitch and the faster the swing, the farther the ball will fly due to conservation of momentum.

Basketball

Basketballs bounce because of the pressurized air inside of them. Gravity pulls the ball down towards the ground, while the extra air pressure pushes against the bottom of the ball, making it push harder against the ground. The arc of releasing a ball, exceeding 33 degrees and putting a back spin on a ball improves the chance of making a shot. The backspin, one puts on the ball while releasing it, allows the ball to travel the slowest possible speed in the air and a less violent rebound. When a player is shooting a ball, he would apply force to the ground by jumping and the force that let him jump also apply to the ball improving the probability of a successful shoot.

Tennis

We can find application of physics in every facet of the game. Design of tennis shoes should take care of force, pressure and friction while design of court shall take care of cushioning and friction. Tennis rackets are designed for power, weight, vibrations and spin. Tennis balls are made keeping in mind the bounce, forces, aerodynamics and spin. The length, composite materials, grips and strings of a racket affect the player's ability to play the sport.

When purchasing a racket, the sweet spot should be one of the biggest deciding factors. There are multiple points on a racket that can be categorized as the sweet spot like center of percussion, vibration node, and center of oscillation. However center of percussion is generally considered the sweet spot. The weight and specifications of a racket are important because the moment, torque and torsion generated by the racket can greatly affect your play. The moment is the cross product of the force of the ball and the distance from the axis of rotation. A racket with a high moment can increase difficulty when volleying and returning, making the racket very difficult to hold while maintaining good positioning. The moment and torque generated give rise to torsion, which is the rotational twist that one feels around the handle's center line that results from each impact. High torsion which is a result of impact, impulse reaction and shock can cause the pain of tennis elbow. It is suggested that a heavier head-light tennis racket with a high swing is the most ideal racket to use for power, control and longevity.

Success in the game of tennis largely comes down to how the racket is wielded and which spot on the racket is used to hit the ball. Spin is important part of winning strategy in tennis. The ball with top spin falls sooner than a ball without top spin. This effect is called the "Magnus effect". While the ball is rotating, a thin layer of air around it is also rotating with it. That means considering the relative velocity of air below it is faster than the velocity of air above it, causing it to fall sooner on the ground.