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Introduction to Biomechanics
Lab 4 & 5  Linear & Angular Impulse and Momentum
Page 1 of 10
Lab #4 & #5  Linear and Angular Impulse and Momentum
Purpose:
The objective of this lab is to understand the linear and angular impulse/momentum relationship. Upon completion
of this lab you will:
•
Understand and know how to calculate positive and negative impulse using both the trapezoidal rule in Excel
and the grid block method.
•
Understand and know how to calculate moment arms, moments of horizontal and vertical forces, and angular
momentum.
•
Be able to plot momenttime curves from a data set.
Introduction:
Many athletic movements, such as the takeoff of a dive, require athletes to generate both linear and angular impulse.
The linear impulse will translate the total body center of mass (TBCM) in the direction of the net linear impulse
relative to the TBCM.
Similarly, the angular impulse will rotate the TBCM in the direction of the net angular
impulse relative to the TBCM.
I. IMPULSE
Linear impulse
represents the effect of a force on a system.
It is defined as the net force acting over a specified time
period.
Linear Impulse =
Σ
F
Δ
t = area under forcetime curve
Figure 1.
An example of horizontal reaction force.
1
1
F
y
forward direction
propulsion impulse
backward direction
braking impulse
changes in braking & propulsion cause a
change in momentum
constant speed = no impulse or change in mv
Propulsive Impulse > Braking Impulse => Increase in velocity
Propulsive Impulse < Braking Impulse => Decrease in velocity
EXSC 408L
Fall ‘08
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View Full DocumentIntroduction to Biomechanics
Lab 4 & 5  Linear & Angular Impulse and Momentum
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Angular impulse
represents the effect of a moment (force acting at a distance from the TBCM) on a system.
It is
defined as the moment of force acting over a specified period of time.
Angular Impulse =
Σ
M
Δ
t = area under momenttime curve
Figure 2. Illustration of a momenttime curve.
A net positive angular impulse indicates that the system will rotate in a counter clockwise direction.
II. MOMENTUM
Linear momentum
represents the quantity of motion that a body possesses. It is defined as the product of the mass of
an object and its velocity.
L = m * v
where
L = linear momentum
m = mass
v = linear velocity
Angular momentum describes the quantity of angular motion. It is defined as the moment of linear momentum.
H = I
cm
*
ω
where
H = angular momentum
I
cm
= moment of inertia about the center of mass
ω
= angular velocity
III. PRINCIPLE OF IMPULSE AND MOMENTUM
The principle of impulse and momentum is a useful concept for understanding the causeeffect relationship between
kinetics (forces) and kinematics (motion). Newton’s Second Law illustrates the basic relationship that
Σ
F = ma
(cause = effect). From this relationship we are able to substitute and rearrange terms to come up with other useful
relationships.
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 '10
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