Ex_rotation-w-p-energy

Ex_rotation-w-p-energy - 2D rigid body dynamics - Work and...

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2D rigid body dynamics - Work and power for rotational motion , () / ave W Pt P τθ τω = = ⋅Δ = 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 2D rigid body dynamics – Energy equation including the rotational motion 111 1 2 2 22 ge g KU U W KU U e +++ = ++ 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 12 k WN s μ = −+ 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 θ up from the horizontal direction. Find the angular velocity of the rod whenit swings down to the vertical position.
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Ex_rotation-w-p-energy - 2D rigid body dynamics - Work and...

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