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

Rotation of a Rigid ObjectAbout a Fixed Axis10

04/18/231 Hamid Salvdari*salvdari@yahoo.com*salvdari.blogfa.com

04/18/232Hamid Salvdari-salvdari@yahoo.com-

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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.

EXAMPLE : Rotating Rod Revisited

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Solution

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EXAMPLE : Connected Cylinders

Solution

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04/18/23

Hamid Salvdari-salvdari@yahoo.com-salvdari.blogfa.com

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

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