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Rotation of a Rigid ObjectAbout a Fixed Axis10
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• 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.
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10.1 Angular Displacement, Velocity, and Acceleration
one radian is the angle subtended by an arc length equal to the radius of the arc.
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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.
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10.2 Rotational Kinematics: Rotational Motion with Constant Angular Acceleration
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EXAMPLE : Rotating Wheel
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Solution
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10.2 Rotational Kinematics: Rotational Motion with Constant Angular Acceleration
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EXAMPLE : CD Player
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Solution
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Solution
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10.4 Rotational Energy
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EXAMPLE : The Oxygen Molecule
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Solution
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EXAMPLE : Four Rotating Masses
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Solution
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10.5 Calculation of Moments of Inertia
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EXAMPLE : Uniform Hoop
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Solution
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EXAMPLE : Uniform Rigid Rod
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Solution
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EXAMPLE : Uniform Solid Cylinder
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Solution
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10.6 Torque
• The tendency of a force to rotate an object about some axis is measured by a vector quantity called torque (tau).
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EXAMPLE : The Net Torque on a Cylinder
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Solution
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10.7 Relationship Between Torque and Angular Acceleration
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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 accelerationangular 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.
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EXAMPLE :Rotating Rod
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Solution
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CONCEPTUAL EXAMPLE
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EXAMPLE : Angular Acceleration of a Wheel
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Solution
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EXAMPLE : Atwood’s Machine Revisited
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Solution
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10.8 Work, Power, and Energy in Rotational Motion
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the radial component of F does no work because it is perpendicular to the displacement.
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EXAMPLE : Rotating Rod Revisited
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Solution
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EXAMPLE : Connected Cylinders
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Solution
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