A heavy flywheel is accelerated (rotationally) by a motor that provides constant

Question

A heavy flywheel is accelerated (rotationally) by a motor that provides constant torque and therefore a constant angular acceleration . The flywheel is assumed to be at rest at time in Parts A and B of this problem. Part A Find the time it takes to accelerate the flywheel to if the angular acceleration is . Express your answer in terms of and . Part B Find the angle through which the flywheel will have turned during the time it takes for it to accelerate from rest up to angular velocity . Express your answer in terms of some or all of the following: , , and . Part C Assume that the motor has accelerated the wheel up to an angular velocity with angular acceleration in time . At this point, the motor is turned off and a brake is applied that decelerates the wheel with a constant angular acceleration of . Find , the time it will take the wheel to stop after the brake is applied (that is, the time for the wheel to reach zero angular velocity). Express your answer in terms of some or all of the following: , , and .

Explanation / Answer

You can apply all the laws of linear motion (F = m*a, momentum = m*v) by using T for F, a for a, ? for v and I (moment of inertia) for m and ? for x. A) ? = ?0 + a*t ?0 = 0, so T_1 = ?_1/a B) ? = 0.5*a*t² = 0.5*a*(?_1/a)² = 0.5*(?_1)²/a C)) ? = ?0 + a'*t; here ?0 = ?_1 . Your question states a' = -5/a but that is not possible. It is either -5*a or -a/5. When the wheel stops, ? = 0 If it is a' = -5*a then 0 = ?_1 - 5*a*t and t = ?_1/(5*a) If it is a' = -a/5 then 0 = ?_1 - (a/5)*t and t = 5*?_1/a

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