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SERCP$118\mathrm{.}4.$P$\mathrm{.}041.$

An approximate model for a ceiling fan consists of a cylindrical disk with four thin rods extending from the disk's center, as in the figure below. The disk has mass $2\mathrm{.}20$ kg and radius $0\mathrm{.}200$ m $.$ Each rod has mass $0\mathrm{.}850$ kg and is $0\mathrm{.}740$ m long.

HINT

$($a$)$ Find the ceiling fan's moment of inertia about a vertical axis through the disk's center. $($Enter your answer in $kg*m^2.)$

$kg*m^2$

$($b$)$ Friction exerts a constant torque of magnitude $0\mathrm{.}111N*m$ on the fan as it rotates. Find the magnitude of the constant torque provided by the fan's motor if the fan starts from rest and takes $15\mathrm{.}0$ s and $17\mathrm{.}5$ full revolutions to reach its maximum speed. $($Enter your answer in N $-$ m$.)$

$$

$N*m$

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