Problem $3$: Propeller coming to rest $(10$ points$)$

A motor is used to spin a submerged propeller that has two blades. When the motor is running, the propeller spins with a constant angular velocity $\backslash (\backslash$omega$\_\{$i$\}=18\mathrm{.}9\backslash$mathrm$\{$rad$\}/\backslash$mathrm$\{$s$\}\backslash )$ in the counterclockwise direction. At some moment of time, the motor shuts off. Suppose that the surrounding water exerts a constant drag force of magnitude $5\mathrm{.}00$ N on each blade, perpendicular to each blade and opposite the direction of rotation, at a point $0\mathrm{.}500$ m from the pivot. The moment of inertia of the propeller is $\backslash ($ I$=198\backslash$mathrm$\{$~kg$\}\backslash$cdot $\backslash$mathrm$\{$~m$\}^\{2\}\backslash ).$ You can neglect gravity in this problem, $($See diagram below.$)$

Hint: Pay careful attention to the signs of your answers in parts $($a$)-($b$).$

$($a$)$ What is the net torque on the whole propeller?

$\backslash (/2\backslash )($b$)$ What is the angular acceleration of the propeller?

$/2.($c$)$ What is the net work done by the surrounding water on the propeller as it comes to rest? Hint: The answer is negative and can be found without solving $($a$)$ and $($b$)$ using a certain theorem that we covered in class. A second way to solve this problem makes use of $($a$),($b$),$ and a bit more.

$($d$)$ How much time does it take for the propeller to come to rest? If you did not solve part $($b$),$ you may assume that the angular acceleration is $\backslash (\backslash$alpha$=-1\mathrm{.}00\backslash$mathrm$\{$rad$\}/\backslash$mathrm$\{$s$\}^\{2\}\backslash )$ for full credit on this part.

Bonus: When the motor is running, what power is the motor delivering to the propeller? $\backslash ($ P$=\backslash$tau $\backslash$omega $\backslash )$