Rotation of a Rigid Object About a Fixed Axis 10 5/25/20151 Hamid

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Presentation transcript:

Rotation of a Rigid Object About a Fixed Axis 10 5/25/20151 Hamid

10.1 Angular Displacement, Velocity, and Acceleration10.2 Rotational Kinematics: Rotational Motion with Constant Angular Acceleration10.3 Angular and Linear Quantities10.4 Rotational Energy10.5 Calculation of Moments of Inertia10.6 Torque10.7 Relationship Between Torque and Angular Acceleration10.8 Work, Power, and Energy in Rotational Motion 5/25/20152 Hamid salvdari.blogfa.com

A rigid object is one that is nondeformable—that is, it is an object in which the separations between all pairs of particles remain constant. In this chapter, we treat the rotation of a rigid object about a fixed axis, which is commonly referred to as pure rotational motion. 5/25/20153 Hamid salvdari.blogfa.com

10.1 Angular Displacement, Velocity, and Acceleration one radian is the angle subtended by an arc length equal to the radius of the arc. 5/25/20154 Hamid salvdari.blogfa.com

5/25/20155 Hamid salvdari.blogfa.com

10.1 Angular Displacement, Velocity, and Acceleration When rotating about a fixed axis, every particle on a rigid object rotates through the same angle and has the same angular speed and the same angular acceleration. 5/25/20156 Hamid salvdari.blogfa.com

10.2 Rotational Kinematics: Rotational Motion with Constant Angular Acceleration 5/25/20157 Hamid salvdari.blogfa.com

EXAMPLE : Rotating Wheel 5/25/20158 Hamid salvdari.blogfa.com

Solution 5/25/20159 Hamid salvdari.blogfa.com

10.2 Rotational Kinematics: Rotational Motion with Constant Angular Acceleration 5/25/ Hamid salvdari.blogfa.com

5/25/ Hamid salvdari.blogfa.com

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EXAMPLE : CD Player 5/25/ Hamid salvdari.blogfa.com

Solution 5/25/ Hamid salvdari.blogfa.com

Solution 5/25/ Hamid salvdari.blogfa.com

10.4 Rotational Energy 5/25/ Hamid salvdari.blogfa.com

EXAMPLE : The Oxygen Molecule 5/25/ Hamid salvdari.blogfa.com

Solution 5/25/ Hamid salvdari.blogfa.com

EXAMPLE : Four Rotating Masses 5/25/ Hamid salvdari.blogfa.com

Solution 5/25/ Hamid salvdari.blogfa.com

10.5 Calculation of Moments of Inertia 5/25/ Hamid salvdari.blogfa.com

EXAMPLE : Uniform Hoop 5/25/ Hamid salvdari.blogfa.com

Solution 5/25/ Hamid salvdari.blogfa.com

EXAMPLE : Uniform Rigid Rod 5/25/ Hamid salvdari.blogfa.com

Solution 5/25/ Hamid salvdari.blogfa.com

EXAMPLE : Uniform Solid Cylinder 5/25/ Hamid salvdari.blogfa.com

Solution 5/25/ Hamid salvdari.blogfa.com

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5/25/ Hamid salvdari.blogfa.com

5/25/ Hamid salvdari.blogfa.com

10.6 Torque The tendency of a force to rotate an object about some axis is measured by a vector quantity called torque (tau). 5/25/ Hamid salvdari.blogfa.com

EXAMPLE : The Net Torque on a Cylinder 5/25/ Hamid salvdari.blogfa.com

Solution 5/25/ Hamid salvdari.blogfa.com

10.7 Relationship Between Torque and Angular Acceleration 5/25/201534

Although each point on a rigid object rotating about a fixed axis may not experience the same – force, – linear acceleration, – linear speed, each point experiences the same angular acceleration angular speed at any instant. Therefore, at any instant the rotating rigid object as a whole is characterized by specific values for o angular acceleration, o net torque, o angular speed. 5/25/ Hamid salvdari.blogfa.com

EXAMPLE :Rotating Rod 5/25/ Hamid salvdari.blogfa.com

Solution 5/25/201537

CONCEPTUAL EXAMPLE 5/25/ Hamid salvdari.blogfa.com

EXAMPLE : Angular Acceleration of a Wheel 5/25/201539

Solution 5/25/201540

EXAMPLE : Atwood’s Machine Revisited 5/25/ Hamid salvdari.blogfa.com

Solution 5/25/ Hamid salvdari.blogfa.com

5/25/ Hamid salvdari.blogfa.com

10.8 Work, Power, and Energy in Rotational Motion 5/25/ Hamid salvdari.blogfa.com the radial component of F does no work because it is perpendicular to the displacement.

EXAMPLE : Rotating Rod Revisited 5/25/ Hamid salvdari.blogfa.com

Solution 5/25/2015 Hamid salvdari.blogfa.com 46

EXAMPLE : Connected Cylinders 5/25/2015 Hamid salvdari.blogfa.com 47

Solution 5/25/201548

5/25/2015 Hamid 49

5/25/2015 Hamid salvdari.blogfa.com 50

5/25/2015 Hamid salvdari.blogfa.com 51

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