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Principle of L inear Impulse and Momentum

Ken Youssefi 1Mechanical Engineering Dept.

dt

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

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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