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Principle of L inear Impulse and Momentum
Ken Youssefi 1Mechanical Engineering Dept.
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vdmF
122
1
vmvmdtFt
t
The Principle of Linear Impulse and Momentum states that the (linear)
impulse from external forces acting on a rigid body over a given time interval
equals the change in linear momentum with respect to the center of mass.
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Principle of Angular impulse and Momentum
Ken Youssefi Mechanical Engineering Dept. 2
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Principle of Angular impulse and Momentum Rigid Body
Ken Youssefi Mechanical Engineering Dept. 3
The Principle of Angular Impulse and Momentum states that the
(angular) impulse from external moments acting on a rigid body
over a given time interval equals the change in angular momentum.
=+
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Principle of I mpulse and Momentum
Ken Youssefi Mechanical Engineering Dept. 4
Impulse and momentum equations for the Planar motion
with rotation about the center of gravity
2D scalar equations
Linear
Angular
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Non-centroidal Rotation
Ken Youssefi Mechanical Engineering Dept. 5
Principle of angular impulse and momentum
Rotation about point O
Use the parallel axis theorem to find
the angular momentum Ho
of the body
about point O.
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Principle of I mpulse and Momentum
Ken Youssefi Mechanical Engineering Dept. 6
The principle can be applied to an entire system of connected
bodies. No need to account for the interaction impulses which
occurs at the connections.
Same reference point, O, should be used to determine the systems
angular impulse and angular momentum
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Conservation of Angular Momentum
Ken Youssefi Mechanical Engineering Dept. 7
The impulses of the external forces are zero when there are
no external forces applied to a rigid body.
Conservation of Linear Momentum of a system
Conservation of Angular Momentum of a system
Diver executing a somersault
(IG)1 = (IG)2 = constant
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Example 1
Ken Youssefi Mechanical Engineering Dept. 8
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Example 1
Ken Youssefi Mechanical Engineering Dept. 9
Principle of impulse and momentum for Gear A
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Example 1
Ken Youssefi Mechanical Engineering Dept. 10
Principle of impulse and momentum for Gear B
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Example 2
Ken Youssefi Mechanical Engineering Dept. 11
Apply the principle of impulse to the sphere at time zero when it comes in contact
with the surface until the time when it starts rolling on the surface.
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Example 2
Ken Youssefi Mechanical Engineering Dept. 12
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Example 2
Ken Youssefi Mechanical Engineering Dept. 13
Substitute tin 2 equation
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Example 3
Ken Youssefi Mechanical Engineering Dept. 14
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Example 3
Ken Youssefi Mechanical Engineering Dept. 15
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Example 3
Ken Youssefi Mechanical Engineering Dept. 16
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Example 4
Ken Youssefi Mechanical Engineering Dept. 17
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Example 4
Ken Youssefi Mechanical Engineering Dept. 18
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Example 4
Ken Youssefi Mechanical Engineering Dept. 19
Mass moment of inertia of the plate about the center of the gravity
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Example 4
Ken Youssefi Mechanical Engineering Dept. 20