Rotation of rigid bodies

Rotation of rigid bodies - 1 Chapter 10: Rotation of Rigid...

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Unformatted text preview: 1 Chapter 10: Rotation of Rigid Bodies Chapter 10: Rotation of Rigid Bodies Rotation of Rigid bodies Rotation of Rigid bodies c A rigid body is an object that is non-deformable. b The separations between all pairs of particles remain constant. b All real objects are deformable to some extent, but the rigid object model is very useful in many situations where the deformation is negligible 2 Angular Position Angular Position c Axis of rotation is the center of the disc c Every particle on the disc undergoes circular motion about a fixed axis of origin O , perpendicular to the plane c Consider a point P located at ( r , ) where r is the distance from the origin to P and is the measured counterclockwise from the reference line c As the particle moves through , it moves though an arc length s . c The arc length and r are related: b s = r s P r c The angular coordinate r s = is in radian 2 rad = 360 r s = 1 rad = = 57.3 Angular Displacement, Velocity Angular Displacement, Velocity c The angular displacement is defined as the angle the object rotates through during some time interval f i = f i f i t t t = = c The average angular speed, , of a rotating rigid object is the ratio of the angular displacement to the time interval c The instantaneous angular speed lim t d t dt = Unit = rad/s dt dx v x = (analogous to ) a c Direction: Right hand rule 3 Angular Acceleration Angular Acceleration c The average angular acceleration, , of an object is defined as the ratio of the change in the angular speed to the time it takes for the object to undergo the change: f i f i t t t = = c The instantaneous angular acceleration is defined as the limit of the average angular acceleration as the time goes to 0 lim t d t dt = Unit = rad/s 2 a a a a Speeding up Speeding down c Direction: c Now suppose can change as a function of time Rotations: Quiz 1 Rotations: Quiz 1 c Bonnie sits on the outer rim of a merry-go-round, and Klyde sits midway between the center and the rim. The merry-go- round makes one complete revolution every two seconds. b Klydes angular velocity is: (a) (a) the same as Bonnies (b) (b) twice Bonnies (c) (c) half Bonnies 4 Rotations: Quiz 1 answer Rotations: Quiz 1 answer c The angular velocity of any point on a solid object rotating about a fixed axis is the same . b Both Bonnie & Klyde go around once (2 radians) every two seconds. b (a) is the correct answer b What will be different? c When a rigid object rotates about a fixed axis in a given time interval, every portion on the object rotates through the same angle in a given time interval and has the same angular speed and the same angular acceleration b So , , all characterize the motion of the entire rigid object as well as the individual particles in the object Rotational Kinematics Rotational Kinematics...
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This note was uploaded on 07/30/2011 for the course PHY 2048 taught by Professor Bose during the Spring '08 term at University of Central Florida.

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Rotation of rigid bodies - 1 Chapter 10: Rotation of Rigid...

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