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CH10%20Rotational%20motion

CH10%20Rotational%20motion - ChapterOutline Chapter10...

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Ch10 Rotation of rigid bodies 1 Nov 11­8:04 AM Chapter 10 Rotation of a Rigid Object about a Fixed Axis Nov 11­8:04 AM Chapter Outline 10.1 Angular Position, Velocity, and Acceleration 10.2 Rotational Kinematics: The Rigid Object Under Constant Angular Acceleration 10.3 Angular and Translational Quantities 10.4 Rotational Kinetic Energy 10.5 Calculation of Moments of Inertia 10.6 Torque 10.7 The Rigid Object Under a Net Torque 10.8 Energy Considerations in Rotational Motion 10.9 Rolling Motion of a Rigid Object Nov 11­8:04 AM Rigid Object A rigid object is one that is nondeformable The relative locations of all particles making up the object remain constant All real objects are deformable to some extent, but the rigid object model is very useful in many situations where the deformation is negligible This simplification allows analysis of the motion of an extended object Nov 11­8:04 AM Angular Position Axis of rotation is the center of the disc Choose a fixed reference line Point P is at a fixed distance r from the origin A small element of the disc can be modeled as a particle at P Nov 11­8:04 AM Angular Position, 2 Point P will rotate about the origin in a circle of radius r Every particle on the disc undergoes circular motion about the origin, O Polar coordinates are convenient to use to represent the position of P (or any other point) P is located at ( r , θ ) where r is the distance from the origin to P and θ is the measured counterclockwise from the reference line Nov 11­8:04 AM Angular Position, 3 As the particle moves, the only coordinate that changes is θ As the particle moves through θ , it moves though an arc length s. The arc length and r are related: s = θ r
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Ch10 Rotation of rigid bodies 2 Nov 11­8:04 AM Radian This can also be expressed as θ is a pure number, but commonly is given the artificial unit, radian One radian is the angle subtended by an arc length equal to the radius of the arc Whenever using rotational equations, you must use angles expressed in radians Nov 11­8:04 AM Conversions Comparing degrees and radians Converting from degrees to radians Nov 11­8:04 AM Angular Position, final We can associate the angle θ with the entire rigid object as well as with an individual particle Remember every particle on the object rotates through the same angle The angular position of the rigid object is the angle θ between the reference line on the object and the fixed reference line in space The fixed reference line in space is often the x­axis Nov 11­8:04 AM Angular Displacement The angular displacement is defined as the angle the object rotates through during some time interval This is the angle that the reference line of length r sweeps out Nov 11­8:04 AM Average Angular Speed The average angular speed, ω avg , of a rotating rigid object is the ratio of the angular displacement to the time interval Nov 11­8:04 AM Instantaneous Angular Speed
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