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2141263 Dynamics & Vibrations, NAV 1 Chapter 5 Plane Kinematics of Rigid Bodies

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Page 1: Chapter 5 Plane Kinematics of Rigid Bodiespioneer.netserv.chula.ac.th/~anopdana/263/51rotation.pdf · Chapter 5 Plane Kinematics of Rigid Bodies. 2141263 Dynamics & Vibrations, NAV

2141263 Dynamics & Vibrations, NAV 1

Chapter 5Plane Kinematics of Rigid Bodies

Page 2: Chapter 5 Plane Kinematics of Rigid Bodiespioneer.netserv.chula.ac.th/~anopdana/263/51rotation.pdf · Chapter 5 Plane Kinematics of Rigid Bodies. 2141263 Dynamics & Vibrations, NAV

2141263 Dynamics & Vibrations, NAV 2

Introduction5.1 Rotation5.2 Absolute Motion5.3 Relative Velocity5.4 Relative Acceleration

5. Plane Kinematics

Page 3: Chapter 5 Plane Kinematics of Rigid Bodiespioneer.netserv.chula.ac.th/~anopdana/263/51rotation.pdf · Chapter 5 Plane Kinematics of Rigid Bodies. 2141263 Dynamics & Vibrations, NAV

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1.1 Introduction5. Plane Kinematics

Particle Rigid Body

Size Small & Not important Big & Important

Motion Translation only Translation and Rotation

Rigid body = a body with negligible deformation= distance between any two points in a rigid body is constant

Page 4: Chapter 5 Plane Kinematics of Rigid Bodiespioneer.netserv.chula.ac.th/~anopdana/263/51rotation.pdf · Chapter 5 Plane Kinematics of Rigid Bodies. 2141263 Dynamics & Vibrations, NAV

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1.2 Motions of a Rigid Body5. Plane Kinematics

1. In space = three dimensions2. In plane = two dimensions

TranslationRectilinearCurvilinear

Rotation

Page 5: Chapter 5 Plane Kinematics of Rigid Bodiespioneer.netserv.chula.ac.th/~anopdana/263/51rotation.pdf · Chapter 5 Plane Kinematics of Rigid Bodies. 2141263 Dynamics & Vibrations, NAV

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1.3 Plane Motions of a Rigid Body5. Plane Kinematics

Translation

Page 6: Chapter 5 Plane Kinematics of Rigid Bodiespioneer.netserv.chula.ac.th/~anopdana/263/51rotation.pdf · Chapter 5 Plane Kinematics of Rigid Bodies. 2141263 Dynamics & Vibrations, NAV

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1.3 Plane Motions of a Rigid BodyRotation

General Plane Motion = Translation + Rotation

5. Plane Kinematics

Page 7: Chapter 5 Plane Kinematics of Rigid Bodiespioneer.netserv.chula.ac.th/~anopdana/263/51rotation.pdf · Chapter 5 Plane Kinematics of Rigid Bodies. 2141263 Dynamics & Vibrations, NAV

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1.3 Plane Motions of a Rigid Body5. Plane Kinematics

Page 8: Chapter 5 Plane Kinematics of Rigid Bodiespioneer.netserv.chula.ac.th/~anopdana/263/51rotation.pdf · Chapter 5 Plane Kinematics of Rigid Bodies. 2141263 Dynamics & Vibrations, NAV

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5-1 Rotation

Page 9: Chapter 5 Plane Kinematics of Rigid Bodiespioneer.netserv.chula.ac.th/~anopdana/263/51rotation.pdf · Chapter 5 Plane Kinematics of Rigid Bodies. 2141263 Dynamics & Vibrations, NAV

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5-1 Rotation

ω as well as α is the same for every point

Page 10: Chapter 5 Plane Kinematics of Rigid Bodiespioneer.netserv.chula.ac.th/~anopdana/263/51rotation.pdf · Chapter 5 Plane Kinematics of Rigid Bodies. 2141263 Dynamics & Vibrations, NAV

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5-1 Rotation

Page 11: Chapter 5 Plane Kinematics of Rigid Bodiespioneer.netserv.chula.ac.th/~anopdana/263/51rotation.pdf · Chapter 5 Plane Kinematics of Rigid Bodies. 2141263 Dynamics & Vibrations, NAV

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1. Rotation about a Fixed Axis

Any point in the body moves in circular motionFor Point A

Note: v and a of other points are different because of different r(ω and α are the same)

5-1 Rotation

Page 12: Chapter 5 Plane Kinematics of Rigid Bodiespioneer.netserv.chula.ac.th/~anopdana/263/51rotation.pdf · Chapter 5 Plane Kinematics of Rigid Bodies. 2141263 Dynamics & Vibrations, NAV

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1. Rotation about a Fixed Axis

Velocity

The equations can be rewritten in a vector form (for plane motion)Direction of ω is given using the right-hand rule.

5-1 Rotation

Page 13: Chapter 5 Plane Kinematics of Rigid Bodiespioneer.netserv.chula.ac.th/~anopdana/263/51rotation.pdf · Chapter 5 Plane Kinematics of Rigid Bodies. 2141263 Dynamics & Vibrations, NAV

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1. Rotation about a Fixed Axis

Acceleration

Direction of α is given using the right-hand rule.

5-1 Rotation

Page 14: Chapter 5 Plane Kinematics of Rigid Bodiespioneer.netserv.chula.ac.th/~anopdana/263/51rotation.pdf · Chapter 5 Plane Kinematics of Rigid Bodies. 2141263 Dynamics & Vibrations, NAV

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Example 1: L-shaped bar5-1 Rotation

Page 15: Chapter 5 Plane Kinematics of Rigid Bodiespioneer.netserv.chula.ac.th/~anopdana/263/51rotation.pdf · Chapter 5 Plane Kinematics of Rigid Bodies. 2141263 Dynamics & Vibrations, NAV

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Example 2:Starting from rest when s = 0, pulley A is given a constant angular acceleration of 6 rad/s2. Determine the speed of block B when it has risen 6 m.

5-1 Rotation