A ceiling fan consists of a small cylindrical disk with 5 thin rods coming from

Question

A ceiling fan consists of a small cylindrical disk with 5 thin rods coming from the center. The disk has mass m_d =2.8 kg and radius R. = 0.26 m. The rods each have mass m_r. = 1.3 kg and length L = 0.72 m. 1) What is the moment of inertia of each rod about the axis of rotation? kg-m^2 2) What is the moment of inertia of the disk about the axis of rotation? kg-m^2 3) What is the moment of inertia of the whole ceiling fan? kg-m^2 4) When the fan is turned on, it takes t = 3.6 s and a total of 14 revolutions to accelerate up to its full speed. What is the magnitude of the angular acceleration? rad/s^2 5) What is the final angular speed of the fan? rad/s 6) What is the final rotational energy of the fan? 7) Now the fan is turned to a lower setting where it ends with half of its rotational energy as before. The time it takes to slow to this new speed is also t = 3.6 s. What is the final angular speed of the fan? rad/s 8) What is the magnitude of the angular acceleration while the fan slows down? rad/s^2

Explanation / Answer

1)
Irod = m*L^2/3
         = 1.3*0.72^2/3
         = 0.225 Kgm^2

2)
I disk = 0.5*m*r^2
           = 0.5*2.8*(0.26)^2
            = 0.095 kgm^2

3)
Itotal = 5*Irod + Idisk
            = 5*0.225 + 0.095
             = 1.22 Kgm^2

4)
d = 14 rev = 14*2*pi rad = 87.96 rad
t = 3.6 s
vi = 0 rad/s
use:
d = vi*t + 0.5*a*t^2
87.96 = 0 + 0.5*a*3.6^2
a = 13.6 rad/s^2

I am allowed to answer only 4 parts at a time

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