**c)**

Constant angular acceleration equation:

ω_{f} = ω_{0} + αt

A heavy flywheel is accelerated (rotationally) by a motor that provides constant torque and therefore a constant angular acceleration *α*.

Assume that the motor has accelerated the wheel up to an angular velocity *ω*_{1} with angular acceleration *α* 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*α*. 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: *ω*_{1}, *α*, and *t*_{1}.

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