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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. 2 1 2 1 Angular position: angle measured from a chosen reference (unit: radians) average angular velocity Angular velocity (unit: rad/s): instantaneous angular velocit y An ave t t t d dt θ θ θ θ ω θ ω Δ = = Δ = 2 1 2 1 2 2 2 average angular acceleration gular acceleration (unit: rad/s ): instantaneous angular acceleration ave t t t d d dt dt ω ω ω α ω θ α Δ = = Δ = = II. Rotation with constant angular acceleration 0 2 0 0 2 2 0 0 1 2 2 ( ) t t t ω ω α θ θ ω α ω ω α θ θ = + = + + = + For rotation with constant angular velocity: 0 0 0, t α ω ω θ θ ω = = = + 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
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