Biomechanics
Biomechanics is the science concerned with the internal and external forces acting on
the human body and the effects produced by these forces. At the highest levels of
sports in which techniques play a major role, improvement comes so often from
careful attention to detail that no coach can afford to leave these details to chance or
guesswork. For such coaches knowledge of biomechanics might be regarded as
essential.
Kinematics
Kinematics is the branch of biomechanics concerned with the study of movement with
reference to the amount of time taken to carry out the activity.
Distance and displacement
Distance and displacement are quantities used to describe the extent of a body's
motion. Distance is the length of the path a body follows and displacement is the
length of a straight line joining the start and finish points e.g. in a 400m race on a
track the length of the path the athlete follows (distance) is 400m but their
displacement will be zero metres (they finish where they start).
Speed and velocity
Speed and velocity describe the rate at which a body moves from one location to
another. These two terms are often thought, incorrectly, to be the same. Average
speed of a body is obtained by dividing the distance by the time taken where as the
average Velocity is obtained by dividing the displacement by the time taken e.g.
consider a swimmer in a 50m race in a 25m length pool who completes the race in 60
seconds - distance is 50m and displacement is 0m (swimmer is back where they
started) so speed is 50/60= 0.83m/s and velocity is 0/60=0 m/s

Speed and Velocity = distance traveled ÷ time taken
Acceleration
Acceleration is defined as the rate at which velocity changes with respect to time.

average acceleration = (final velocity - initial velocity) ÷ elapsed time
From Newton's 2nd law:
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
Force = Mass x Acceleration
Acceleration = Force ÷ Mass
If the mass of a sprinter is 70kg and the force exerted on the starting blocks is 700N
then acceleration = 700 ÷ 70 = 10 msec²
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Acceleration due to gravity
Whilst a body is in the air it is subject to a downward acceleration, due to gravity, of
approximately 9.81m/s²
Vectors and scalars
Distance and speed can be described in terms of magnitude and are known as scalars.
Displacement, velocity and acceleration that require magnitude and direction are
known as vectors.
Components of a vector
Figure 2
Figure 1
Let us consider the horizontal and vertical components of velocity of the shot in
Figure 1.
Figure 2 indicates the angle of release of the shot at 35° and the velocity at release as
12 m/sec.


Vertical component Vv = 12 x sin 35° = 6.88 m/sec
Horizontal component Vh = 12 x cos 35° = 9.82 m/sec
Let us now consider the distance the shot will travel horizontally (its displacement).
Range (R) = ((v² × sinØ × cosØ) + (v × cosØ × sqrt((v × sinØ)² + 2gh))) ÷ g
Where v = 12, Ø = 35, h = 2m (height of the shot above the ground at release) and g =
9.81


R = ((12² × sin35 × cos35) + (12 × cos35 × sqrt((12 × sin35)² + 2x9.81x2))) ÷
9.81
R = 16.22m
The time of flight of the shot can be determined from the equation (2 × v × sinØ) ÷ g
2

Time of flight = (2 x 12 x sin 35) ÷ 9.81 = 1.4 seconds
Uniformly accelerated motion
When a body experiences the same acceleration throughout some interval of time, its
acceleration is said to be constant or uniform. In these circumstances, the following
equations apply:


Final velocity = initial velocity + (acceleration x time)
Distance = (initial velocity x time) + (½ x acceleration x time²)
Moment of force (torque)
The moment of force or torque is defined as the application of a force at a
perpendicular distance to a joint or point of rotation.
Angular Kinematics
Angular distance and displacement
When a rotating body moves from one position to another, the angular distance
through which it moves is equal to the length of the angular path. The angular
displacement that a rotating body experiences is equal in magnitude to the angle
between the initial and final position of the body.
Angular movement is usually expressed in radians where 1 radian = 57.3°
Angular speed, velocity and acceleration



Angular speed = angular displacement ÷ time
Angular velocity = angular displacement ÷ time
Angular acceleration = (final angular velocity - initial angular velocity) ÷ time
Angular Momentum
Angular momentum is defined as: angular velocity x moment of inertia
The angular momentum of a system remains constant throughout a movement
provided nothing outside the system acts with a turning moment on it. This is known
as the Law Conservation of Angular Momentum. In simple terms, this means that if a
skater, when already spinning, changes their moment of inertia (they move their arms
out to the side) then the rate of spin will change but the angular momentum will stay
the same.
Linear Kinetics
Kinetics is concerned with what causes a body to move the way it does.
Momentum, inertia, mass, weight and force
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



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Momentum: mass x velocity
Inertia: the resistance to acceleration - reluctance of a body to change
whatever it is doing
Mass: the quantity of matter of which a body is composed of - not affected by
gravity - measured in kilograms (kg)
Weight: force due to gravity - is mass x gravity (9.81m/s²)
Force: a pushing a pulling action that causes a change of state (rest/motion) of
a body - is proportional to mass x acceleration - is measured in Newtons (N)
where 1N is the force that will produce an acceleration of 1 m/s² in a body of
1kg mass
The classification of forces, external or internal, depends on the definition of the
'system'. In biomechanics, the body is seen as the 'system' so any force exerted by one
part of the system on another is known as an internal force all other forces are
external.
Newton's Laws of Motion
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
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First Law: Every body continues in its state of rest or motion in a straight line
unless compelled to change that state by external forces exerted upon it.
Second Law: The rate of change of momentum of a body is proportional to the
force causing it and the change takes place in the direction in which the force
acts
Third Law: To every action there is an equal and opposite reaction OR for
every force that is exerted by one body on another there is an equal and
opposite force exerted by the second body on the first
Newton's law of gravitation

Any two particles of matter attract one another with a force directly
proportional to the product of their masses and inversely proportional to the
square of the distance between them
Work, Energy and Power
Kinetic energy is mechanical energy possessed by any moving object. An equation for
Kinetic Energy can be derived from the work definition:

Work = force x distance moved in the direction of the force
Kinetic Energy = ½ x mass x velocity² (result is in joules)
Power is defined as the rate at which energy is used or created from other forms



Power = energy used ÷ time taken
Power = (force x distance) ÷ time taken
Power = force x velocity
Angular Kinetics
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Translation and couple
A force that acts through the centre of a body result in only translation. A force whose
line of action does not pass through the body's centre of gravity is called an eccentric
force and results in translation and rotation.
Example - if you push through the centre of an object it will move forward in the
direction of the force (translation) if you push to one side of the object (eccentric
force) it will move forward and rotate.
A couple is an arrangement of two equal and opposite forces that cause a body to
rotate.
Levers
A lever is a rigid structure, hinged at one point and to which forces are applied at two
other points. The hinge or pivot point is known as the fulcrum. One of the forces that
act on the lever is known as the weight that opposes movement and the other is the
force that causes movement. For more details see the page on Levers.
Bernoulli Effect
Lift forces interact with objects in flight and are caused by the aerodynamic shape of
the object. If an object has a curved top and flat bottom (wing of an aircraft), the air
will have further to travel over the top than the bottom. For the two airflows to reach
the back of the object at the same time the air flowing over the top of the object will
have to flow faster. This means that there will be less pressure above the object (air is
thinner) than below it and the object will lift. This is often referred to as the Bernoulli
effect.
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