phy2048-ch10

phy2048-ch10 - Chapter 10 Rotation and Rolling I Rotational...

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Chapter 10 – Rotation and Rolling II. Rotation with constant angular acceleration III. Relation between linear and angular variables - Position, speed, acceleration I. Rotational variables - Angular position, displacement, velocity, acceleration IV. Kinetic energy of rotation V. Rotational inertia VI. Torque VII. Newton’s second law for rotation VIII. Work and rotational kinetic energy IX. Rolling motion

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I. Rotational variables Rigid body: body that can rotate with all its parts locked together and without shape changes. r s radius length arc = = θ Rotation axis: every point of a body moves in a circle whose center lies on the rotation axis. Every point moves through the same angle during a particular time interval. Angular position: the angle of the reference line relative to the positive direction of the x-axis. Units: radians (rad) Reference line: fixed in the body, perpendicular to the rotation axis and rotating with the body.
rev rad rad r r rev 159 . 0 3 . 57 1 2 2 360 1 = = = = = o o π Note: we do not reset θ to zero with each complete rotation of the reference line about the rotation axis. 2 turns Æ θ =4 π Translation: body’s movement described by x(t). Rotation: body’s movement given by θ (t) = angular position of the body’s reference line as function of time. Angular displacement: body’s rotation about its axis changing the angular position from θ 1 to θ 2 . 1 2 θ = Clockwise rotation Æ negative Counterclockwise rotation Æ positive Angular velocity: t t t avg = = ω 1 2 1 2 dt d t t = = 0 lim Average: Instantaneous: Units: rad/s or rev/s

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These equations hold not only for the rotating rigid body as a whole but also for every particle of that body because they are all locked together. Angular speed ( ω ): magnitude of the angular velocity. Angular acceleration: t t t avg = = ω α 1 2 1 2 dt d t t = = 0 lim Average: Instantaneous: Angular quantities are “normally” vector quantities Æ right hand rule. Object rotates around the direction of the vector Æ a vector defines an axis of rotation not the direction in which something is moving. Examples: angular velocity, angular acceleration
Angular quantities are “normally” vector quantities Æ right hand rule.

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This note was uploaded on 07/30/2011 for the course PHY 2049 taught by Professor Saha during the Spring '08 term at University of Central Florida.

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phy2048-ch10 - Chapter 10 Rotation and Rolling I Rotational...

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