Physics of Sports
P.K. Thiruvikraman
Sports and academics do not go together, at least in the minds of most parents in India. While they do know that all work and no play will make Jack, Ahmed or Hari a dull boy, they view sports as something which takes up precious time which can be devoted to studies. So it might come as a surprise to some if they are told that there is lot of science which is used while playing sports. Even professional sportspersons may be using some scientifi c principles in their sporting activities without realizing it.
In this article, I will try to illustrate the applications of some principles of physics in various sports and games. The motivations for this article are two-fold. On the one hand, it can motivate students who do not relish physics to realize some of its practical applications in the sporting arena. On the other, those who are keen sportspersons can think about how they can profitably utilize scientific principles in their sporting activities.
The high jump
Those who have watched international athletic events on television would surely have been amazed by the way the high jump is executed by international athletes. The jumper, as expected, runs towards the bar, but instead of approaching the bar in a headon fashion, he approaches it at an angle so that when he is very close to the bar, it is his/her back which is facing the bar! He/she then jumps upwards and actually backwards, bending his/her body into an arch (see figure). This jumping style is known as the ”Fosbury flop” after the American athlete, Dick Fosbury who executed it for the first time in the 1968 Olympics held in Mexico city. Prior to this, athletes straddled the bar so that when they went over the bar their body was almost horizontal and parallel to the bar.
Fosbury showed that a greater height could be cleared by using his technique when compared to the western roll or straddling technique. The figure given alongside shows the path of the centre of gravity (C.G) of the athlete executing the high jump. It is seen that the centre of gravity of the athlete is always below the bar at all points of time. So even though the athlete goes above the bar, his centre of gravity remains below the bar! The work done by the athlete in executing a jump is determined by the height through which his C.G is raised. So the athlete using the flop technique shown below will spend less energy than those athletes who use other techniques. The height to which the sportsperson’s C.G is raised is determined by his/her velocity (in the upward direction) when he leaves the ground. So even if the athlete leaves the ground with a lower speed (which means he can exert lesser force) he/she is able to clear a greater height! A similar technique is also used in case of the pole vault.
Spin in cricket and tennis
Cricket enthusiasts will know that the bowler with the highest number of wickets in test cricket is not a fast bowler, but a spinner. In fact, the bowler with the next highest number of wickets is also a spinner! Even though batsmen fear fast bowlers for the physical damage they can cause, spinners are not feared to a lesser extent. How does the spinner make the ball “turn”?
Even amateur cricketers will of course know the rudiments of this art, but let us dive into the mysteries of spin bowling.
There are essentially two variants of spin bowling, known as finger spin and wrist spin. In both cases, the final result is that when the bowler releases the ball, he/she will not only give the ball a velocity in the direction of the batsman, but also cause it to rotate. What is the consequence of this rotation? Let us imagine a cricket ball which has been imparted some spin such that it is seen to be rotating clockwise (as seen by the bowler). When the ball lands on the ground, friction between the ball and the ground will not only slow down the ball, but oppose its rotation (during the short time when the ball hits the ground). Since the ball was rotating lockwise, the frictional force due to the ground will act in the opposite direction (which would be to the right of the bowler). This force will cause the ball to deviate or “turn” to the right (as seen by the bowler). If the bowler was a right hander this kind of spin is imparted by the fingers. To make the ball turn in the opposite direction, a right hand bowler would have to use his/her wrist (this is more effective than trying to use the fingers).
What determines the amount of turn, i.e., deviation of the ball? There are multiple factors at play here. One is the rotational velocity of the ball and the other is the frictional force between the ball and the ground. The frictional force is greater if both surfaces (ball and ground) are rough. This is why spinners are more effective with an old ball and when the cricket pitch has become rough due to constant use.
In addition to the two types of spin described here, a third variety is “top spin”. This is when the spin axis is perpendicular to the direction of motion (see figure below). This means the angular (or spin) velocity of the ball adds to the normal velocity. Therefore, when the ball lands, the frictional force opposing both these motions acts in the forward direction! As a result, the ball comes off faster after bouncing on the ground! This can be nasty surprise for the batsman!
Top spin can also be easily imparted to a tennis or table tennis ball with the same result. The ball will not only increase in speed after bouncing but will bounce higher (due to the increased speed). Top spin is imparted to the tennis (or TT) ball by hitting the ball at an angle instead of hitting it with the full face of the racket. The side of the racket facing the ball will be facing slightly down and will “pass over” the ball after hitting it.
In tennis (or table tennis), in addition to top spin, one can also “slice” the ball which causes the rotation direction to be reversed. This will cause the ball to slow down further after bouncing. It will also bounce up to a lower height because of this.
In addition to spin another feared weapon in the armoury of a bowler is “swing”. Swing is also used by footballers. When a cricket or football swings, it deviates, but unlike in the case of spin described earlier, the deviation is in the air. This deviation can be explained by invoking the Bernoulli’s principle. According to Bernoulli’s principle, a moving fluid (like air) exerts less sideways pressure when it is moving faster. Suppose a footballer imparts some rotational velocity to the ball when kicking it. Let us say it is spinning anti-clockwise (as seen from the top). Then the air (which is moving relative to the ball) will move faster on one side compared to the other side. This is because the rotational velocity of the ball adds to the speed of the air on one side and opposes it on the other side. Therefore, the ball will deviate towards the side with lower pressure (where the relative speed of the air is higher). This effect is used by footballers to make the ball travel in an arc or in other words, to bend it like Beckham (one of the famous exponents of this art).
The Bernoulli principle also has a role to play in the case of top spin and slice mentioned above. In the case of top spin, the ball dips towards the ground, while in the case of slice it travels further in the air.
A cricket ball can be made to swing, not by imparting it spin (like a football), but because the ball is not a perfect sphere. It is a sphere with a seam (a bunch of threads connect the two hemispheres which form the cricket ball). By keeping the seam at an angle to the direction of motion of the ball, the bowler introduces an asymmetry between the two sides of the ball. Therefore, the speed of the air which is flowing past the ball on the two sides will be different, causing the ball to deviate in the air (as expected from Bernoulli’s principle). The deviation is increased by increasing the asymmetry between the two sides of the ball. This is done by making one side of the ball rougher and/or the other side smoother. This is why we see cricketers rubbing the ball on their trousers or applying saliva (ugh!) before a ball is bowled.
I am sure one can come up with many more examples of applications of physics in sports. This article only illustrates a few examples.
Note: All figures given here are reproduced from Wikipedia commons.
The author has been teaching physics for the last 18 years. While he was fascinated by both movies and sports from childhood, he has recently begun using them for teaching physics. In addition to physics, movies, and sports, he is also interested in reading about other topics. He welcomes feedback on this article through thiru@hyderabad.bits-pilani.ac.in.
