14 - 2D Rigi body rotation kinematics - Rotation about a fixed pivot

14 - 2D Rigi body rotation kinematics - Rotation about a fixed pivot

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2D Rigid Body Kinematics – Rotation about a fixed pivot I. General rotation Rotation of a rigid body: change of orientation of any arbitrary line on the body. 21 Angular position: angle measured from a chosen reference (unit: radians) average angular velocity Angular velocity (unit: rad/s): instantaneous angular velocit y An ave tt t d dt θ θθ ω Δ == Δ− = 2 2 2 average angular acceleration gular acceleration (unit: rad/s ): instantaneous angular acceleration ave t dd dt dt α Δ II. Rotation with constant angular acceleration 0 2 00 22 1 2 2( ) t ωω α θω ωα =+ =+ + For rotation with constant angular velocity: 0 0 0, t ωω = = Example A rotating wheel has an angular velocity of 10 rad/s at t = 0. The wheel starts to accelerate with a constant angular acceleration of 6 rad/s 2 for 5 s, and then slows down with a constant deceleration. The wheel rotates through a total angle of 325 rad from t = 0 to the time it stops. Find the angular deceleration of the wheel and total time of rotation.
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This note was uploaded on 10/17/2009 for the course PHYS 2305 taught by Professor Tschang during the Spring '08 term at Virginia Tech.

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14 - 2D Rigi body rotation kinematics - Rotation about a fixed pivot

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