Motion

Motion is defined as the change of location or position of an object with respect to time i.e. in order to analyse motion accurately, you need to describe the position of a body, and the time between its successive positions. When we talk about a “body” we refer to both inanimate objects (such as sporting equipment) and animate objects (human body or parts of). To create motion a force must be applied to an object. The force can be applied internally from within the body (e.g. muscular contraction of the quadriceps causes the lower leg to rotate) or externally (the foot strikes the ball).

linear motion

Linear motion occurs when a body moves in a straight line when all parts of it travel exactly the same distance, in the same direction, in the same time e.g. an archer’s arrow in flight moving towards a target. We can see how linear motion is achieved when a golf ball is travelling into the hole on the green. The golfer will hit the ball through its centre of mass so travels in a straight line into the hole.

Speed = distance/time (s =d/t)

Velocity = displacement/time or distance/time (m/s)

Acceleration = (final velocity – initial velocity)/time taken (m/s²)

Speed, Velocity and Acceleration

Speed is defined as the rate at which a body moves from one location to another, in everyday language it is used to describe how fast an object is travelling. The average speed of a body is obtained by dividing distance covered by time taken and is calculated as:

Speed = Length of path / Time (Units: metres per second) (m.s ^-1 OR m/s)

The unit that speed is presented in is dependent on the units that the distance and time are presented in; for athletics races the distances are recorded in meters and times in seconds as such the units for speed are presented in meters per second and written as m.s^-1

Velocity is defined as the rate at which an object changes its position. Thus, velocity is speed, with a direction and is a vector quantity. When presenting velocity the same rules are applied as presenting speed (i.e. m.s^-1) and when calculating velocity the following equation can be used:

Velocity = Displacement / Time (Units: metres per second) m.s ^-1 OR m/s

If it takes a swimmer 20 seconds to finish a 100m race then their average speed and velocity will be the same (i.e. 50 m ÷ 10 seconds = 10 m.sec-1. However, if a swimmer completed 100m by swimming two lengths in a 50m pool, in 50 seconds: In this case, their average speed will be = 2 m.sec-1 (100 ÷ 50). But their average velocity will be 0 m.sec-1 because their finish position is the same as the start so there is in effect no displacement

Why Speed is a Scalar Quantity and Velocity a Vector Quantity

Because these two terms are used interchangeably by most people (those that aren’t scientists mostly!) it can be sometimes confusing to know the difference. As speed is a scalar quantity it only has magnitude. This means that it can be used to describe any object that is moving. For example, a rally car may be travelling at 100 kmh, it doesn’t matter in what direction it is moving. However, when using the term velocity, a direction of travel must be included (although this doesn’t always happen when most people speak). So if the car was travelling in an easterly direction then velocity could be used. Sometimes scientists refer to speed being the scalar magnitude of velocity.

Acceleration

The ability to accelerate rapidly is crucial for success in most games. However, in most games the ability to decelerate rapidly, especially when changing direction means that performers must be able to exert large muscular forces to slow and stop their momentum and alter their running direction; therefore having good agility. Acceleration is defined as the rate at which velocity changes with respect to time and is calculated using the following equation:

As an example, 10 minutes into a bike race you are riding a bike up a hill with a constant velocity of 10m.sec^-1 and you reached the top where the course levelled out. It took you 5 seconds to increase your velocity to 20m.sec^-1, which means that you accelerated at 2m.sec^-2 to reach this new velocity.

When presenting acceleration m.s^-2 are the units. If you were to state the units then it would be 2 metres per second per second because velocity (already m.s-1) is divided by time (in seconds). Therefore to avoid using this ‘wordy’ unit, metres per second squared is used.

Angular motion

Angular motion occurs when a basketball player spins a ball on their finger or a gymnast rotates around a parallel bar we see angular motion in action. Angular motion occurs when an object moves around axis; this can be around an external axis (e.g. the gymnast around the bar) or an internal axis (e.g. the ball rotating around its centre of mass). Angular motion occurs whenever a force applied to an object with a fixed axis of rotation, like when your biceps brachii contracts to cause flexion at the elbow joint to lift the dumbbell.

Angular Momentum

As Newton’s 1^st law predicts that if an object was moving in space it would continue to move at the same velocity unless a force acts upon it. The same could be said for objects rotating in space, if you were spun around you would continue to spin (and spin and spin and spin), we also have evidence for this with the earth rotating and making night and day! When an object rotates it has angular momentum, which is a quantity of the angular motion of an object. It is a product of the velocity it is rotating at and moment of inertia, which is shown as the following equation:

Angular momentum = moment of inertia x angular velocity

When discussing Newton’s laws and angular momentum it is common to use the term ‘angular analogues of Newton’s laws of motion’.

The moment of inertia is the resistance of an object to rotate and is rotational equivalent of mass. The moment of inertia depends upon;

the mass of the object, the more mass the larger the moment of inertia,
the distribution of the mass away from the axis of rotation, the further away the mass is from axis of rotation the greater the moment of inertia.

A playground roundabout spinning will have more angular momentum if it is spinning faster (greater angular velocity) and if there are more people on the roundabout (greater mass and moment of inertia). The more people on the roundabout the more force is required to start the roundabout because there is a larger moment of inertia. Based on the equation the greater the moment of inertia the greater the angular momentum thus it would take more force to stop the roundabout if there is greater angular momentum.

Examples of Moment of Inertia

RUNNING: By bending the leg on recovery, it is easier for the quadriceps to lift a bent leg due to a lower moment of inertia.

HURDLING: By bending the trailing leg lifting towards the trunk, it can be moved much faster over the hurdle.

POLE VAULTING: Flexing the legs on the swing phase toward the bar enables the body to rotate much quicker and easier.

Angular Momentum

The quantity of angular momentum which a body possesses about an axis of rotation in known as its angular momentum. Angular momentum is equal to the product of the moment of inertia of a body & its angular velocity.

Angular momentum enables us to explain why the rate of spin (angular velocity) changes when the moment of inertia changes. This is because angular momentum of a system remains constant throughout a movement provided nothing outside the system acts with a turning moment on it. This phenomenon is the Law of Conservation of Angular Momentum.

In many sports, being able to rotate the body quickly can be an important factor in determines success. For example, in gymnastics, high diving and trampolining double tucked somersaults score more ‘difficulty’ or ‘tariff’ marks than only rotating once. To rotate faster an individual can apply more force upon take-off but once in the air they cannot change their angular momentum. However, by bringing body parts closer to the axis of rotation (e.g. performing a tuck), they can decrease the moment of inertia and increase angular velocity (rotate faster). In trampolining, there is a certain amount of time a performer is in the air and this depends on the height they are bouncing. However, being able to tuck into a tight position may mean that a performer could perform a double, rather than just a single somersault, therefore as long as their form is good they will be awarded more marks for their routine

This shows how angular velocity, moment of inertia change at different stages of a dive with a back somersault, as well as showing how there is conservation of angular momentum once they are in the air.

Conservation of Angular Momentum

When analysing somersault actions and other skills that involve angular momentum it is important to understand how moment of inertia and angular velocity interact to maintain or conserve angular momentum. Once a diver leaves the springboard when they are performing a somersaulting dive, angular momentum cannot be changed unless an external force is applied to them. However, to enable the diver to rotate faster when they are in the air they can assume a tucked position. On the springboard, the moment of inertia is high because they have a straight body position and the mass of their extremities is far from their axis of rotation. This means that they will leave the board with a relatively slow angular velocity. However, tucking decreases the moment of inertia and this results in an increase in angular velocity. The diver will need to enter the water in a straight and controlled way to score highly so to slow the rotation they will open up to increase the moment of inertia, which decreases the rate they are rotating and makes it easier to finish the dive well.

Application to Other Sports

An ice skater performing an axel (twisting jump where they rotate around their longitudinal axis) uses exactly the same principles once they are in flight. By reducing the moment of inertia the skater increases angular velocity; bringing their arms into the body allowing rate of spin to increase. When they are landing this skill they adduct their arms so their mass is further away from their axis, the moment of inertia increases and the angular velocity decreases so the skaters find it easier to land safely. In table tennis you may notice that many players are now tucking their non-bat holding arm close to their chest possibly because keeping this arm tucked in reduces the moment of inertia and this makes it easier to begin shots like a topspin or loop shot.

Projectile motion

In athletic throwing events performers aim to throw the javelin, shot, discus or hammer further than their competitors to win. When one of these objects leaves a performer’s hand it becomes a ‘projectile’, but so does a long jumper once they have left the take-off board! All objects do not fly through the air similarly, you just have to look how a Frisbee flies compared to a shot putt to see a difference! In throwing events there are specific factors that determine how far an object will travel:

Its initial velocity – which depends on two things:
1. The speed of the run up, which is especially important for javelin throwing as the velocity the thrower is travelling upon the javelin being released is added to the forces provided by the rest of the body.
2. The force applied to the object (more specifically the impulse – see later). Therefore, throwers with more explosive strength are likely to be able to transfer more force from their muscular contractions.
The height of release; the more height at release the more horizontal distance, therefore taller athletes have advantage over short ones in throwing events.
The angle of release will play a major role in the distance thrown. The optimal angle of release is usually calculated to be 4° to maximize horizontal distance. However, in reality there are few objects that should be released at this angle. Balls struck from the floor may fit this recommendation but when objects are released higher than they will land a lower angle is recommended, approximately 43-44^o for a hammer thrower). The optimum angle of release for a discuss is usually only about between 35 and 40^o which is because of the Bernoulli effect.
Angle of attack
Drag
Applying some spin to a discus can help to improve the distance thrown, as long as the angle of attack is correct. However, many novices do not apply forces through the CoM of a javelin and cause angular momentum so that the javelin turns over end-over-end. This spin can massively increase air resistance and the distance thrown.
Air resistance – this has a negligible effect on most objects if thrown correctly. However, in discuss throwing if the ‘angle of attack’ is not correct then air resistance and drag can reduce the distance it travels.
Gravity - gravitational forces affect the vertical motion of an object and because gravity affects heavier objects more, lighter ones will usually travel further.

EXAM TIP: Do not use the term WIND resistance to describe air resistance

The influence of air resistance changes depending on:

Object mass and surface area
Projectile speed - generally the speed of release has the greatest influence on projectile range than angle/height of release
Influence of any motions of the projectile other than direction of flight, e.g. topspin, backspin, hooking, slicing
Surface covering the projectile

As air resistance acts on horizontal component, it is this component that needs to be increased to compensate for air resistance. Hence, the greater the air resistance the lower the angle of release.

A golf balls surface is covered with dimples so can effect the flight of the ball by the application of spin and fluid mechanics. However, the air resistance for a golf ball in flight is minimal so is often regarded as negligible.

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As air resistance acts on horizontal component, it is this component that needs to be increased to compensate for air resistance. Hence, the greater the air resistance the lower the angle of release.

This table shows the different optimal angles of release for different sports. When the projectile lands at a lower level than at take-off, e.g. long jump, the optimum angle is always less than 45º and vice versa.

Vertical projection - speed of a projectile decreases gradually to zero at maximum height of the throw. Gravity causes the object to return to the ground.

Horizontal projection - the angle of release determines the height a projectile reaches.

Parabolic flight curves

The flight path of a projectile without aerodynamic properties or without spin will fly in a parabolic manner. This means that when drawing the flight path it will look like a curve where the left and right sides match or mirror each other similar to a symmetrical inverted U shape. One example of an object that will not fly in a parabolic fashion is a shuttle cock, which air resistance does affect, reducing the horizontal motion and making it drop sooner than something like a tennis ball.