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). Express your answer in terms of some or all of the following: omega_1, alpha, and t_1. 4 years ago Report Abuse

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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