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 alpha. The flywheel is assumed to be at rest at time t = 0 in Parts A and B of this problem.

1) Find the time t_1 it takes to accelerate the flywheel to omega_1 if the angular acceleration is alpha.


2) Find the angle theta_1 through which the flywheel will have turned during the time it takes for it to accelerate from rest up to angular velocity omega_1.

3) Assume that the motor has accelerated the wheel up to an angular velocity omega_1 with angular acceleration alpha 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 -5lpha. 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).

Explanation / Answer

1) Find the time t_1 it takes to accelerate the flywheel to omega_1 if the angular acceleration is alpha. omega_1 = 0 + alpha x t_1 t_1 = omega_1 / alpha ....................................ans 2) theta_1 = 0 + 0.5 x alpha x ( omega_1 / alpha )^2 = 0.5 (omega_1)^2 / alpha ....................................ans 3) 0 = omega_1 - 5lpha x t_2 t_2 = ( omega_1 ) ( alpha ) / 5................................ans

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