phy2048-ch9_new - Chapter 9 – Rotation and Rolling II...

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Unformatted text preview: Chapter 9 – 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 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 . 3 . 57 1 2 2 360 1 = = = = = r r π π Note: we do not reset θ to zero with each complete rotation of the reference line about the rotation axis. 2 turns b 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 θ θ- = Δ Clockwise rotation b negative Counterclockwise rotation b positive Angular velocity: t t t avg Δ Δ =-- = θ θ θ ω 1 2 1 2 dt d t t θ θ ω = Δ Δ = → Δ lim Average: Instantaneous: Units: rad/s or rev/s 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 Δ Δ =-- = ω ω ω α 1 2 1 2 dt d t t ω ω α = Δ Δ = → Δ lim Average: Instantaneous: Angular quantities are “normally” vector quantities b right hand rule. Object rotates around the direction of the vector b a vector defines an axis of rotation not the direction in which something is moving....
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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-ch9_new - Chapter 9 – Rotation and Rolling II...

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