Tennis Ball
Spin on a tennis ball is an important factor for the players as it increases or decreases the flight of the ball through the action of magnus force. Magnus force is obtained by the interaction of the spinning ball and the air molecules of the top and bottom half of the ball. This magnus force basically gives the ball it’s flight and tennis players can manipulate these physics concept to benefit their games. Depending on where the magnus effect is most effective will determine the height of the flight and also the bounce.
Torque, the spinning result of a force is applied onto the ball, causing it to spin. During topspin force is exerted on top of the ball, this is done by hitting the top of the ball with the tennis racquet giving it a torque effect clockwise. In contrast to underspin, where force is exerted at the bottom of the ball to make it spin anticlockwise. The number of spins can be increased by increasing the amount of force applied as explained by the equation: .This can be increased by decreasing the coefficient of friction between the ball and the strings of the racquet. When the ball hits the racquet it makes the main strings flex, therefore the spring gains elastic potential energy as it is stretched. Once the ball leaves the racquet the elastic potential energy gained by the spring is exerted into the tennis ball, making it go forward with a spin when hit at a specific angle. This is called the snap back effect. Decreasing the amount of cross strings on the racquet will decrease the friction on both bodies. A low coefficient friction means that there are less disturbance on the snap back effect, thus, more force can be exerted on the ball. An increase in force will directly increase the torque of the ball. If greater torque force is applied, the ball will be able to spin more.
Increasing the amount of spin on the ball will affect the duration of the flight. The type of spin also determines the height and duration of the trajectory. Magnus force is the force which gives the ball its flight through the interaction of the spinning ball and the air around. This interaction creates an unequal drag force at the top and bottom. In topspin there is less pressure at the top of the ball and thus a higher velocity. This is because the direction of the spin is corresponding with the direction of flight. This means that there is less drag force – the motion of the ball is the same as the fluid or air in this case that’s surrounding it, this is consistent with less pressure. In contrast to the bottom of the ball where the drag is greater and thus a greater pressure and less velocity. This is because the the ball is spinning in the opposite direction as the direction of the air. Because the bottom of the ball has greater pressure than the top of the ball, this will result in the drag being more dominant upwards, like so.
Because there is a drag force upwards, this will correspond to a force that pulls the ball downwards. This can be explained by Newton’s 3rd Law, which states that for a force exerted will result in an opposite and equal force. The force that opposes the drag force is called the magnus force. Because this force is downward, the ball’s vertical flight will be shorter.
How magnus effect is created where it is most effective (downwards or upwards) in underspin is opposite to the topspin. In underspin the top has greater drag force and thus a greater pressure. This is because the ball is spinning anticlockwise and in the opposite direction of the air, this creates a greater drag. Whilst at the bottom of the ball the drag is less and thus a smaller pressure. The bottom of the ball’s tangential velocity is in the same direction as the direction of flight. The bottom of the ball has a greater velocity too. Because the drag is more effective downwards and according to Newton’s 3rd Law there will be a force upwards – which is also the magnus force. Therefore the flight of a ball with underspin will have greater vertical height because there is an additional force upwards. But this upward force will only encourage losing control of the ball therefore the player will most likely hit the ball below the net height.
Depending on the amount of spin the ball will obtained will determine the duration of the flight. The more spins there will be, the more effective the magnus force will be for a longer time. This is because the spins creates the magnus force. This is why the spinning factor of a ball is greatly significant.
The type of spin also determines the balls bounce when it hits the ground. This is due to the spin change after the bounce into topspin. When a ball with underspin gets in contact with the ground, they create a friction through this interaction. The friction occurring here is kinetic friction force because both the ground and ball is in motion, this friction opposes the horizontal motion. What this friction force does is it alters the rotation of the ball from underspin to topspin. This shift will need greater force thus, the friction kinetic force will be more effective on the ball for longer, enlarging the total net friction force. Because this is occurring, the horizontal velocity of the ball is decreasing due to the friction that acts on the opposite direction. If the horizontal velocity is slow the corresponding vertical velocity will be much steeper. This also occurs due to the energy loss to heat energy and sound through the long contact of the ground and the ball. Therefore, if the horizontal velocity is reduced, the ball will rebound from the ground with a larger angle from the ground. As explained prior, in attempt to control a ball with underspin, tennis players tend to decrease the height of the ball. This will result in a smaller incident angle and smaller rebound angle – although still larger than the incident angle. Thus, in reality, it really doesn’t bound that much higher.
In underspin there is great net friction force, this is in contrast to topspin where the friction force is reduced. This can be done when a ball with smaller tangential velocity in relevance to the horizontal velocity hits the ground. The friction is in the direction to the right (remains constant for either shots), this direction will encourage the direction of angular velocity on the topspin ball and therefore, increasing the angular velocity. If the angular velocity increased, the tangential velocity must also as described by the equation: Vt=wr. Angular velocity is the measure of how fast a ball is rotating and or changing its position on the rotational motion. While tangential velocity is the velocity of the ball that is obtained from any point of the ball. Once this increase in tangential velocity is increased and is equal to the horizontal velocity of the ball, this will result in a biting or rolling condition. Because both tangential and horizontal velocity corresponds each other the total friction is much less. This means that the horizontal velocity is greater than the vertical velocity, therefore the ball will bounce at a height that is less than the incident.
Like the bounce in a ball with underspin, the reality is a little different when put into context. We know that topspin has an additional downwards force (magnus force), therefore tennis player will tend to make the height of its trajectory greater. Consequently, it will hit the ground at a greater angle and with greater gravitational energy, thus, the bounce will be higher. But the bounce vertical height will remain lower than the angle at which the ball hit the ground. This is beneficial for the player who used the shot as it will be harder for the opposing player to hit it again due to the large bounce.
High Diver
The force to be able to perform spins during a high dive is obtained prior to when the diver is about to jump off. They gain torque during this section that allows them to increase the angular momentum. The meaning of angular momentum is a rotating object or body’s inclination to remain in rotational motion. Also the angular momentum is conserved throughout a divers flight unless torque is applied during the flight – conservation of angular momentum, but torque can’t be gained during the flight, therefore the jump is really important. Assuming the diver uses springboards to jump off from, they will be able to gain momentum by bouncing on the spring boards. If they have imply greater mass onto the board, the weight force can be increased according to the equation: F=mg. If the weight force that pull downwards is great, an opposing force of the same magnitude will be present – as stated by Newton’s 3rd Law. In context the diver will gain more force to be able to spin. Torque’s equation is: , this means if the force is increased the greater its turning effect or torque will be. And if torque is increased, the diver can rotate from their axis of rotation which is the centre of their body, hence spins are created.
The number of spins can be maximised by increased decreasing the rotational inertia. We know that the angular momentum is conserved during the flight, thus, we must change the moment of inertia according to the equation: L=Iw. Decreasing the moment of inertia means that less torque force is required to spin the object, this will result in an increase of angular velocity – the rate of the angle changing during its rotational motion. Therefore, less torque or angular momentum is required to perform spins and hence, maximising it and since the energy is conserved. In context, the diver can decrease rotational inertia by compressing the body into a ball. This means bringing the body close to the stomach or otherwise called the centre/axis of rotation. If the body was to be spread, they will be more exposed to air friction.
We can compare two contrasting dive to further explain this idea. Straight dive has the greatest moment of inertia because the body is fully spread and has the largest radius from the centre of rotation. If the moment of inertia – which is the tendency to resist the rotational motion is great and angular momentum can’t be increased it will be difficult to perform more spins. This is because the moment of inertia is increasing while the angular momentum is conserved since the initial dive.
This is opposite to the tuck dive where the diver is able to perform many spins due to their tuck position. In this tuck position the diver’s body is compressed towards the centre/axis of rotation, this decreases the moment of inertia. If the moment of inertia is decreased the diver won’t need as much angular momentum to increase their angular velocity since angular momentum is also conserved. Thus, they will spin at a faster rate and will be able to fit in more spins during their flight.
High Jump
Rotation of a high jumper can be initiated by the approach run and take off. This section of the competition is significant because it is where the vertical velocity can be increased and where the angular momentum is gained (this component is conserved throughout the jumper’s flight). The approach run must have great velocity so that the jumper can gain sufficient vertical velocity. By doing this the force will be applied a lot longer. The take off section must involve a lot of bend, this lowers the position of the centre of mass, this means that the weight force is increased. And as described by Newton’s 3rd Law, an equal and opposite force will act against this weight force. Thus, there is force vertical and if the athlete is bending while running, the horizontal velocity will be transferred to vertical velocity. Combining these ideas and assuming that the athlete leaves the mat at an appropriate angle, angular momentum can be gained. The forces and angular momentum gained in this section allows the athlete to rotate. The most popular type of jump is the Fosbury Flop. This type of jump is the most effective because the centre of mass is below the bar. We can also consider centre of mass as the centre of gravity, this is the location where all weight force is most effective. When the athlete jumps over the bar, their body curves around the bar. This is due to the angular momentum they obtained during their take off. Because angular momentum is applied, when one body part is moving with greater velocity – in this jump it would be the lowered shoulder, another both part must be moving at a slower rate – the knees that are elevated. Due to this curve the weight force of the body is acting downwards, therefore the centre of gravity and thus, the centre of mass is below the bar. Just like any other curved objects the centre of mass is outside the body. Due to this technique, less force is required to get over the bar. This is especially important since energy is conserved during the flight. Because less rotational force is required, the excess force can be used to further curve the back and lift up the stomach. This will result in a better performance, as there are more chance that the athlete won’t touch the bar.
If an athlete was to use the straddle technique – this is the technique where the jumper lifts one leg across the bar and forces the rest of the body to get over the bar, more force will be required to lift up their centre of mass. This technique is less effective in producing better performance when compared to Fosbury flop. This is because the centre of mass is remained within the athlete, this means that more force is required to get over the bar. Since energy is conserved throughout the jump, this type of jump is highly disadvantageous. Also because it requires a lot of force, the athlete will not be able to curve their body around the bar, making it more risky for them to touch the bar and lose the game. This is why the Fosbury flop is highly advantageous, because it doesn’t require as much force, thus this force can be used to further curve the body and avoid touching the bar.