Transcript Linear kinematics

ESS 303 – Biomechanics
Linear Kinematics
Linear VS Angular
Linear: in a straight
line (from point A to
A
point B)
Angular: rotational
A
(from angle A to
angle B)
B
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 systems
2D: X & Y axis
3D: X, Y & Z axis
Linear Kinematics
B
A
What About This?
B
A
What About This?
B
A
Some Terms
Position: location in space relative to a
reference
Scalars and vectors
Scalar 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?
Distance & Speed
B
Displacement & Velocity
A
Graph Basics
B (4,3)
Y
A (1,1)
C (5,2)
D (2,1)
X
SI Units
Systeme International d’Units
Standard units used in science
Typically metric
Mass: 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)/s
 Acceleration 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 / t
 Velocity = Δ position / Δ t
 Acceleration = Δ V / Δ t
 Slope = rise / run
 Resultant = √(X2 + Y2)
 Remember: A2 + B2 = C2
 SOH CAH TOA
 Sin θ = Y component / hypotenuse
 Cos θ = X component / hypotenuse
 Tan θ = Y component / X component
θ
Sample Problems
A swimmer completes 4 lengths of a
50m pool
What distance was traveled?
What was the swimmer’s displacement?
Move from point (3,5) to point (6,8) on a
graph
What 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 seconds
What 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 ground
What was the vertical component of
velocity?
What was the horizontal component of
velocity?