Biomechanics – Module 1:
Module 1.1 - Intro:
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Biomechanics is the study of forces and their effects on living systems.
Broken into two branches:
o Kinematics (study of temporal and spatial factors) – WHAT
 Distance/displacement
 Speed/velocity
 Consistency of movement (acceleration)
 Linear & angular movement
o Kinetics (causes of motion) HOW
 Force
 Friction
 Impulse
Goals of biomechanics WHY
o Improve performance (better technique  greater biomechanical efficiency)
o Reduce risk of injury (better technique  safer methodology)
Module 1.1.1 – Types of Motion:
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Linear Motion
o When the whole body/object moves in the same direction and distance
o Linear motion can be:
 Rectilinear (whole body/object moves in a straight line)
 Curvilinear (whole body/object moves along a curved path)
Angular Motion
o When the whole body/object follows a circular path with an axis of rotation
(point which the body/object rotates).
General Motion (most common)
o The combination of linear and angular motion, e.g., when walking: the limbs
rotate around the joints while the centre of mass travels along a linear path.
Module 1.1.2 – Units of Measurement:
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In biomechanics we use the International System of Units (SI units)  metric system.
Units of measurement consist of:
o Fundamental (independent of any other unit)
 E.g. metres, seconds, kilograms
o Derived (units derived by dividing/multiplying a fundamental unit)
 Centimetres, millisecond, grams, metres per second.
Weight vs Mass:
o Mass  amount of matter in a body (measure in kg)
o Weight  force exerted by a mass due to gravity (measure in Newtons (N))
Module 1.1.3 – Scalar & Vector Quantities:
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Physical quantities can be either:
o Scalar (magnitude only  e.g., 4m/s)
o Vector (magnitude and direction  4m/s North)
Distance and Displacement:
o Distance (d – scalar quantity)  length of the path
o Displacement (s – vector quantity)  length of a straight line joining the star
and end points.
Speed and Velocity:
o Speed (sp – time rate change of distance - scalar)
o Velocity (v – time rate change of displacement - vector)
o Average vs Instantaneous Speed/Velocity:
 Average  the average of all instantaneous speeds/velocities
calculated over time, e.g. total distance div time gives avg.
 Instantaneous  the speed/velocity at any given instant in time, e.g.,
speedometer.
Acceleration:
o Acceleration (a - time rate change of velocity – vector)
o Different algebraic symbols to represent initial velocity (u) and final velocity
(v), thus;
o Signs and conventions:
 For magnitude of acceleration:
 Positive (+)  speeding up
 Negative (-)  slowing down
 ALSO implies direction  if an object is falling it has a
negative direction.
Module 1.2 – Working with Vectors
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It’s common for multiple vectors to be acting on a body at the same time, thus, we
need to add/subtract vectors to find the net effect on the system.
Drawing vectors:
o Vectors are represented by straight arrows, detailing the direction (which way
it’s pointing) and the magnitude (the length of the arrow).
Module 1.2.1 – Vector Addition (in one plane):
Module 1.2.2 – Vector Addition (in two planes):
Steps:
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Draw the head of the vertical arrow connected to the tail of the horizontal arrow.
Create a right angled triangle by drawing the resultant line (R) – the hypotenuse.
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Solve for theta (placed in the angle of the tail of the vertical, aka where the diagram
started) using inverse sohcahtoa. (often using tan).
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Write answer as: (length of resultant) (angle of theta) 8m S60°15’W.
Module 1.2.3 – Resolving Vectors into Components:
Steps:
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Multiply the magnitude of the arrow by cosine(angle between the arrow and variable
line your solving for). E.g., 40m/s × cos(60).
Module 1.3 – Graphing
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Graphing allows for data visualisation and interpretation.
Tangents:
o A straight line that touches the curve at one point only:
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o The gradient of the tangent represents the gradient of the curve at that
particular point.
Area Principle:
o Finding the area below a curve is known as integration.
o To do integration you break the curve down into geometric shapes such as
rectangles and triangles as well as using the trapezoidal rule.
Module 1.3.1 - Kinematic/Time Graphs
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Kinematic/time graphs represent kinematic data (y axis) against time (x axis).
These include:
o Displacement/time graphs
o Velocity/time graphs
o Acceleration/time graphs
Module 1.3.2 – Displacement/Time Graphs
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Gradient of a displacement/time graph:
o
Module 1.3.3 – Velocity/Time Graphs
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Gradient of a velocity/time graph:
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o The area under a velocity-time curve = displacement, given by
Module 1.3.4 – Acceleration/Time Graphs
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Area under an acceleration/time graph = velocity, given by 𝟐 𝒂𝒕.
𝟏
𝟐
𝒗𝒕.