\\\textup{A flywheel turns through } 40 \textup{rev as it slows from an angular speed of 1.5 rad/s to a stop.}
\\\textup{a) Assuming a constant angular acceleration, find the time for it to come to rest.}
\\\indent\Delta \Theta = 20 \textup{rev} = 40 \textup{rad}
\\\indent\omega _i = 1.5 rad/s
\\\indent\omega _f = 0 rad/s
\\\indent\Delta \Theta = \frac{1}{2}(\omega_i+\omega_f)t
\\\indent80pi=\frac{1}{2}(1.5)t
\\\indent t=\frac{160\pi}{1.5}= 340 s
\\\textup{b) What is its angular acceleration?}
\\\indent\omega_f=\omega_i+\alpha t
\\\indent0=1.5+\alpha(340)
\\\indent\alpha=-.0044 rad/s^2
\\\textup{c) How much time is required for it to complete the first 20 of the 40 revolutions?}
\\\indent\Delta \theta = 40 \pi rad
\\\indent\Delta \theta = \omega_it+\frac{1}{2}\alpha t^2
\\\indent y=-.022t^2+1.5t-40\pi
\\\indent\textup{From graph, two solution: 98s and 584s. } t_4_0_r_e_v > t_2_0_r_e_v \textup{ so 584s is an extraneous solution.}
\\\indent t=98s