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Absolute Motion
Lecture 10
ME 231: Dynamics
2
Question of the Day
ME 231: Dynamics
The cable reel rolls without slipping on the horizontal surface. Point A on the cable has a velocity vA = 0.8 m/s to the right.
Compute the velocity of the center O and the angular velocity �� of the reel.
3
Outline for Today
� Question of the day� Absolute-motion analysis� Geometric relations� Maintaining consistent sense� Absolute motion: exercise(s)� Answer your questions!
ME 231: Dynamics
� Question of the day
4
Absolute-Motion Analysis
� The method relates the position of a point, A, on a rigid body to the angular position, ��, of a linecontained in the body
� The velocity and acceleration of point Aare obtained in terms of the angular velocity, �, and angular acceleration, �, of the rigid body
ME 231: Dynamics
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Recall: Constrained Motionof Connected Particles
� Application of absolute-motion analysis
� Successive differentiation of cable length
� Geometric relations are simple (i.e., linear variables only)
ME 231: Dynamics
yx �� 20 ��yx ���� 20 ��
BA vv 20 ��
BA aa 20 ��
bryrxL ����� 12 22
��Constraint Equations
66
�
�
Geometric Relations
ME 231: Dynamics
Linear � Position� Velocity� Acceleration
Angular� Position� Velocity� Acceleration
y
xz
Rigid-body motion includes both linearand angular variables
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Maintaining Consistent Sense
ME 231: Dynamics
��
���� ���
dtd
����� ��� ���� 2
2
dtd
dtd
� Angular position of moving line is specified by counter-clockwise angle (�)
� Angular velocity (�) is positive in the same counter-clockwisesense
� Angular acceleration (�) is positive in the same counter-clockwise sense
A key concept in dynamics!
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Outline for Today
� Question of the day� Absolute-motion analysis� Geometric relations� Maintaining consistent sense� Absolute motion: exercise(s)� Answer your questions!
ME 231: Dynamics
� Question of the day� Absolute-motion analysis� Geometric relations� Maintaining consistent sense
9
Absolute Motion: Exercise
A wheel of radius rrolls without slipping.
Determine the wheel’s angular motion in terms of the linear motion of its center O.
Also determine the acceleration of point C on the rim of the wheel as it contacts the ground.
ME 231: Dynamics
10
Absolute Motion: Another Exercise
Determine the angular velocity of bar AB in terms of the linear position of displacement xA.
ME 231: Dynamics
Slider A moves horizontally with a constant speed v.
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Absolute Motion: Yet Another Exercise
Derive an expression for the upward velocity of the car hoist in terms of ��.
ME 231: Dynamics
The piston rod of the hydraulic cylinder is extending at the rate s.
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Outline for Today
� Question of the day� Absolute-motion analysis� Geometric relations� Maintaining consistent sense� Absolute motion: exercise(s)� Answer your questions!
ME 231: Dynamics
� Question of the day� Absolute-motion analysis� Geometric relations� Maintaining consistent sense� Absolute motion: exercise(s)
13
Homework Survey
ME 231: Dynamics
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Homework Survey
ME 231: Dynamics
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For Next Time…
� Begin Homework #4 due next Thursday (9/20)
� Read Chapter 6, Section 6.2
ME 231: Dynamics