(Solved): An approximate model for a ceiling fan consists of a cylindrical disk with four thin rods extending ...

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 2.40 kg and radius 0.200 m . Each rod has mass 0.850 kg and is 0.860 m long. (a) Find the ceiling fan's moment of inertia about a vertical axis through the disk's center. (Enter your answer in \( \mathrm{kg} \cdot \mathrm{m}^{2} \).) \( \times \mathrm{kg} \cdot \mathrm{m}^{2} \) (b) Friction exerts a constant torque of magnitude \( 0.111 \mathrm{~N} \cdot \mathrm{~m} \) 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 15.0 s and 19.5 full revolutions to reach its maximum speed. (Enter your answer in \( \mathrm{N} \cdot \mathrm{m} \).) \[ \mathrm{N} \cdot \mathrm{~m} \]