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 B Find the angle ?_1 through which the flywheel will have turned during the time it takes for it to accelerate from rest up to angular velocity ?_1. Express your answer in terms of some or all of the following: ?_1, ?, and t_1 Part C Assume that the motor has accelerated the wheel up to an angular velocity ?_1 with angular acceleration ? in time t_1 . At this point, the motor is turned off and a brake is applied that decelerates the wheel with a constant angular acceleration of -5?. Find t_2 , 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: ?_1, ?, and t_1

Explanation / Answer

( heta_{1} = omega_{1}t_{1} + 1/2lpha t_{1}^{2})

using the equations of motion of an angular body we get the above equation

(omega_{f} = omega_{i} - 5lpha t)

(omega _{i} = omega_{1} + lpha t_{1})

now to stop omega final is to be zero so

(t_{2} = omega_{i}/5lpha )

(t_{2} =(omega_{1} + lpha t_{1})/5lpha)

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