hw11solution - Homework 11 Solution CHANG 1 The first stage...

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Homework 11 Solution CHANG 1 The first stage of rotation has a constant angular acceleration, so at the end of stage 1 the angular velocity 1 and angular position 1 can be formulated as: 1 0 1 t 1 0   20 20 1 0 0 t 1 1 2 1 t 1 2 0 0 1 2   20 2 200 In the second stage the rotation has constant angular velocity, so we know 2 1 and 2 0. At the end of the 60-second rotation, we can set up the total angle of rotation to be 1 1 t 2 4000 200 20   60 20 4 rad/s 2 CHANG 2 There are three parts in the entire rotation: the accelerating stage, constant velocity stage, and the decelerating stage. We first find the angular velocity 1 and the angular position 1 at the end of the first accelerating stage, with 0 0: 0 t 1 0 1 t 1 0 5 8 40 rad/s 0 0 t 1 2 t 2 1 0 0 t 1 1 2 1 t 1 2 1 2 5 8 2 160 rad Since the angular velocity remains constant for stage 2, at the end of the second part of the rotation the angular velocity 2 and angular position 2 can be found to be 2 1 40 rad/s 2 1 1 t 2 160 40 10 560 rad
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