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18 - 2D rigid body rotational kinetics - Work, power, and energy equation

18 - 2D rigid body rotational kinetics - Work, power, and energy equation

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2D Rigid Body Rotational Kinetics – Work, Power, and Energy equation Work and power for rotational motion , for constant torqu e W P τ θ τ ω = ⋅Δ = is the angle of rotation or angular displacement ( )/ ave W d P t τ θ τ θ θ = = ⋅Δ Δ Δ e Example A disk with mass 15 Kg and radius 0.4 m is pivoted at its center. A constant torque of 30 Nm supplied by a motor turns the disk from rest. (a) Calculate the work produced by the motor from t = 0 to t = 8 s. (b) Find the average power provided by the motor from t = 0 to t = 8 s. (c) Find the instantaneous power output of the motor at t = 8 s. Ans : (a) 24 kJ (b) 3 kW (c) 6 kW – Energy equation including the rotational motion 1 1 1 1 2 2 2 2 g e g K U U W K U U + + + = + + Rotational kinetic energy K = (1/2) I ω 2 Translational kinetic energy K = (1/2) m υ 2 Gravitational potential energy U g = mgy cm Elastic potential energy U e = (1/2) kx 2 1 2 k W N s μ τ θ = − + Example 1. The slender rod of mass m and length L is pivoted at point O , and it is released from rest as shown at an angle
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