ESS 303 – Biomechanics Linear Kinematics. Linear VS Angular Linear: in a straight line (from point...
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Transcript of ESS 303 – Biomechanics Linear Kinematics. Linear VS Angular Linear: in a straight line (from point...
ESS 303 – Biomechanics
Linear Kinematics
Linear VS Angular
Linear: in a
straight line (from
point A to point B)
Angular: rotational
(from angle A to
angle B)
A B
A
B
Kinematics VS Kinetics
Kinematics: description of motion
without regard for underlying forces
Acceleration
Velocity
Position
Kinetics: determination of the
underlying causes of motion (i.e., forces)
Linear Kinematics
The branch of biomechanics that deals with the description of the linear spatial and temporal components of motion
Describes transitional motion (from point A to point B)
Uses reference systems2D: X & Y axis3D: X, Y & Z axis
Linear Kinematics
A
B
What About This?
A
B
What About This?
A
B
Some Terms
Position: location in space relative to a reference
Scalars and vectorsScalar quantities: described fully by
magnitude (mass, distance, volume, etc)
Vectors: magnitude and direction (the position of an arrow indicates direction and the length indicates magnitude)
Some Terms
Distance: the linear measurement of space between points
Displacement: area over which motion occurred, straight line between a starting and ending point
Speed: distance per unit time (distance/time)Velocity: displacement per unit time or
change in position divided by change in time (displacement/time)
What About This?
A
BDistance & SpeedDistance & Speed
Displacement & VelocityDisplacement & Velocity
Graph Basics
A (1,1)
B (4,3)
C (5,2)
D (2,1)
X
Y
SI Units
Systeme International d’Units
Standard units used in science
Typically metricMass: Kilograms
Distance: Meters
Time: Seconds
Temperature: Celsius or kalvin
More Terms
Acceleration: change in velocity divided by change in time (Δ V / Δ t) (m/s)/sAcceleration of gravity: 9.81m/s2
Differentiation: the mathematical process of calculating complex results from simple data (e.g., using velocity and time to calculate acceleration)
Derivative: the solution from differentiation Integration: the opposite of differentiation (e.g.,
calculation of distance from velocity and time)
Today’s Formulas
Speed = d / tVelocity = Δ position / Δ tAcceleration = Δ V / Δ tSlope = rise / runResultant = √(X2 + Y2)
Remember: A2 + B2 = C2
SOH CAH TOASin θ = Y component / hypotenuseCos θ = X component / hypotenuseTan θ = Y component / X component θ
Sample Problems
A swimmer completes 4 lengths of a 50m poolWhat distance was traveled?What was the swimmer’s displacement?
Move from point (3,5) to point (6,8) on a graphWhat was the horizontal displacement?What was the vertical displacement?What was the resultant displacement?
Sample Problems
A runner accelerates from 0m/s to 4.7m/s in 3.2 secondsWhat was the runner’s rate of acceleration?
Someone kicks a football so that it travels at a velocity of 29.7m/s at an angle of 22° above the groundWhat was the vertical component of
velocity?What was the horizontal component of
velocity?