Lecture
8
Vector Mechanics for Engineers:
Dynamics
MECN 3010
Department of Mechanical Engineering
Inter American University of Puerto Rico
Bayamon Campus
Dr. Omar E. Meza Castillo
omeza@bayamon.inter.edu
http://www.bc.inter.edu/facultad/omeza
Inter - Bayamon
MECN 3010
Tentative Lecture Schedule
Topic
Lecture
Kinematics of a Particle
1,2,3,4
Kinetics of a Particle: Force and Acceleration
5
Kinetics of a Particle: Work and Energy
6
Planar Kinematics of a Rigid Body
7
Planar Kinematics of a Rigid Body
8
2
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"Lo peor es educar por métodos basados
en el temor, la fuerza, la autoridad,
porque se destruye la sinceridad y la
confianza, y sólo se consigue una falsa
sumisión”
Einstein Albert
Topic 5: Planar Kinematics of
a Rigid Body
MECN 3010
Force and Acceleration
3
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MECN 3010
Chapter Objectives
 To introduce the methods used to
determine the mass moment of inertia of
a body.
 To discuss applications of these equations
to bodies undergoing translation, rotation
about a fixed axis, and general plane
motion.
4
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MECN 3010
17.1 Mass Moment of Inertia
5
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MECN 3010
17.1 Mass Moment of Inertia: Procedure for Analysis
6
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17.1 Mass Moment of Inertia
Parallel-Axis Theorem: If the
moment of inertia of the
body about an axis passing
through the body’s mass
center in known, then the
moment of inertia about any
other parallel axis can be
determined by using the
parallel-axis theorem.


I   r 2 dm   d  x '  y'2 dm
m

2
m

  x '2  y'2 dm  2d  x ' dm  d 2  dm
MECN 3010
m
m
I  I G  md 2
m
7
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17.1 Mass Moment of Inertia
Radius
of
Gyration:
Occasionally, the moment of
inertia of a body about a
specified axis is reported in
handbooks using the radius
of gyration, k. This is a
geometrical property which
has unit of length. When it
and the body’s mass m are
known the body’s moment
of inertia is determined from
the equation
I  mk 2 or k 
I
m
MECN 3010
Composite Bodies:
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9
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10
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12
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13
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14
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15
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17.2 Planar Kinetic Equations of Motion
MECN 3010
 Equation of Translational Motion
This equation is referred to as the translational
equation of motion for the mass center of a rigid
body. It states that the sum of all the external
forces acting on the body is equal to the body's
mass times the acceleration of its mass center G
17
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MECN 3010
17.2 Planar Kinetic Equations of Motion
18
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MECN 3010
17.2 Planar Kinetic Equations of Motion
 Equation of Translational Motion
19
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MECN 3010
17.2 Planar Kinetic Equations of Motion
20
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MECN 3010
17.2 Planar Kinetic Equations of Motion
21
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MECN 3010
17.2 Planar Kinetic Equations of Motion
22
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MECN 3010
17.2 Planar Kinetic Equations of Motion
 General Application of the Equations of
Motion
23
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MECN 3010
17.3 Equations of Motion: Translation
 Rectilinear Translation
24
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MECN 3010
17.3 Equations of Motion: Translation
 Curvilinear Translation
25
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26
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27
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17.4 Equations of Motion: Translation
 Equations of Motion : Rotation about a
Fixed Axis
31
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MECN 3010
17.4 Equations of Motion: Translation
 Equations of Motion : General Plane
Motion
32
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MECN 3010
Homework6  Blackboard
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