The equation for this is force / area = pressure. In sport this can be explained using long jump landing. If you land on your feet it will apply more pressure to your joints and the sand leaving a bigger indent in comparison to feet. If you land on your back then it will leave a more life like indent and apply less pressure to the body.
Reaction forces – This is related to Newton’s 3rd law that states for every action there is an equal reaction. When you push the ground the ground pushes back with allows us to move. This works the same in running when the athlete hits the ground, the ground produces the same amount of force back which allows them to sprint. Fig 1.2 shows how this concept works.
(Fig 1.2)
Equilibrium – equilibrium is a balance of forces. A body is said to be at equilibrium if it is still or moving with uniform velocity. In a 400m run if there is one point where all forces balance out then this is equilibrium.
Magnitude – this is basically size, it can be measured in different units. In most sports the unit is metres like the 400m example completed by subject A.
“The property of relative size or extent (whether large or small)”
Linear motion: is when all points on a body move the same distance, in the same direction, and at the same time.
Displacement – this is a vector quantity that refers to how far an object has moved. In sport if an athlete completed a 400m race they would have a displacement of 0m.
Vectors – are quantities described by both magnitude and direction. If athlete ran 100m north this is a vector measurement.
Scalars – are quantities described only by size or magnitude. If an athlete ran 100m this is a scalar measurement.
Velocity – is a vector quantity that refers to the rate at which an object changes in position. If someone was jumping front and back they may be moving very fast but there velocity would be zero as they always end up in the same position. This is shown in the equation which is (displacement/time = velocity mps). In the data from subject A we ran the 400m on a straight peace of land. This means that the speed and velocity are both the same in this situation. Below is some data of different speed/ velocity at different points throughout the race. If we measure the velocity over smaller and smaller intervals we will eventually get instantaneous velocity.
Speed / Velocity (Fig 1.3)
0-100 / 100 = 7.52 m/s
13.29
100-150 / 50 _ = 7.58 m/s
6.59
300-350 / 50 _ = 5.63 m/s
8.87
0-400 / 400 = 6.46 m/s
61.91
Acceleration – is a vector quantity, it is the rate at which an object changes its velocity. An object can accelerate positively or negatively (decelerating). In a 400m run to find out the acceleration I would take away the velocity at the end of the race from the velocity at the beginning of the race the divide it by the time taken to find the average acceleration. The equation for acceleration is final velocity – initial velocity / time.
I am going to work out the average acceleration for 400m for subject A. at the start of the race he is not moving so his initial velocity is zero. His final velocity was 6.46 m/s as shown in Fig 1.3. The difference is 6.46 m/s which then need to be divided by the time (61. 91s). 6.46 / 61.91 = 0.10 m/s2. If I kept doing this equation over smaller and smaller distances I would eventually find the instantaneous acceleration.
Mass and gravity:
Centre of mass – first I will try and explain what mass is. Mass is the amount of matter an object has, measured in kg. This is different to weight which is due to the gravity acting on your body so your weight will change from earth to the moon but your mass will stay the same. The (COM) is the same as the (COG) in most environments. It is only when you are comparing between the earth and the moon that they would be different.
Centre of gravity – this is the point at which gravity is said to act on the body. It is a point where the body’s weight is evenly distributed. In a sprint start the (COG) is as far forward as it will go before the object topples. This is so that gravity is pulling them forward which help them build up momentum.
Inertia – this is the resistance against a force. The more mass an object has, the more inertia or difficulty to move that object has. Things with a lot of inertia are harder to get moving and also harder to stop. They are harder to stop because they build up more momentum.
In sumo wrestling the competitors try and give themselves a lot of inertia. They do this by having a large mass which is mostly disturbed at the lower part of there body. They also spread there arms and legs out to lower there centre of gravity which gives them more inertia.
Angular motion: occurs around an axis that can be within the body or outside the body.
Rotation - occurs around an axis that can be within the body or outside the body. As you may have guessed rotation is also known as angular motion.
This is like the rotation at the elbow when doing a bicep curl. The joint rotates so that you can left the weight.
Angular displacement – this is just the same as displacement but it is around an angle. To be scientifically correct angles should not be measured in degrees, but in RADIANS (r)
Angle = arc length
Radius of arc
360 degrees = 2 x pi radians = 6.28 radians
- 180o = pi r = 3.14 r
- 90o = 1/2 pi r = 1.57 r
- 30o = 1/6 pi r = 0.52 r
This is like in the discus when you use your arm as a lever and you body as an axis. You rotate your body to the point of release. If you spin around once before releasing the discus you have completed 6.28 radians.
Angular velocity – is measured in angle turned through per second not metres per second.
Angular velocity = angle turned through
Time taken
Angular velocity is the rate of spin, most easily understood as revolutions per second (revs per sec).
Revs per sec would have to be converted to the unit radians per second (rs-1) for calculations
1 rev per second = 2 x pi = 6.28 rs-1
This is used when an ice skater spins on the ice and completes one revolution in a certain amount of time. They can speed up or slow down there rate of spin by changing there body shape.
Angular acceleration - rate of change of angular velocity
Angular acceleration = change of angular velocity
Time taken
This is used when rates of spin increase or decrease. Like in an ice skater you would first find out the change in angular velocity and then divide this by the time it has taken. This will give you the angular acceleration for the skater. It is the speed at which his rate of spin changes so as he spins faster his acceleration will go up and as he slows down he will be decelerating.
Moment of inertia – This is the equivalent of mass, for a rotating system/object. It is also known as rotational inertia as it is how the inertia of an object affects it rate of spin.
Objects rotating with large MI require large torque to change their angular velocity. Objects with small MI require small torque to change their angular velocity.
MI depends on the spread of mass away from the axis of spin, hence body shape the more spread out the mass, the bigger the MI. That is why sumo wrestlers have there legs wide apart and lower there body so they have large MI.
If you have your arms held out you have twice as much inertia then when you have them down by your side. The further the mass is away from the axis of rotation increases the MI dramatically. That is why you what to spread you mass out.
Like an ice skater when there arms are spread out wide they have a higher moment of inertia which slows down the rate at which they spin. When they lift there arms above there head they lower there moment of inertia which increases there rate of spin.
Torque – this is also known as the moment of force, it is the turning effect produced by a force.
“Torque is defined as the application of a force at a perpendicular distance to a joint or point of rotation.”
If torque acts on a spinning object it will change its angular velocity. The object can speed up or slow down. In dancing the partner will spin the partner just below the wrist so they have a better lever as the lever arm is longer then if the spun them by the shoulder.
Conservation of momentum - It is well known that the momentum of an object will stay the same provided no external force acts on it. This works the same way with angular momentum, a spinning body will remain the same (provided no external forces act).
A body which is spinning will keep its value of angular momentum once the movement has started. Therefore if MI (moment of inertia) (I) changes by changing body shape then angular velocity must also change to keep angular momentum (H) the same. If MI (I) increases (body spread out more) then angular velocity must decrease (rate of spin gets less). Like an ice skater when there arms are spread out wide they have a higher moment of inertia which slows down the rate at which they spin. When they lift there arms above there head they lower there moment of inertia which increases there rate of spin.
