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 md 3.3 kg and radius R 0.26 m. The rods each have mass mr 1.2 kg and length L 0.71 m. 1) What is the moment of inertia of each rod about the axis of rotation? 201 kg-m2 Submit ) What is the moment of inertia of the disk about the axis of rotation? kg-m2 Submit 3) What is the moment of inertia of the whole ceiling fan? kg-m2 Submit 4) When the fan is turned on, it takes t 3.1 s and a total of 13 revolutions to accelerate up to its full speed. What is the magnitude of the angular acceleration? rad/s2 Submit 5) What is the final angular speed of the fan? rad/s Submit 6) What is the final rotational energy of the fan?

Explanation / Answer

1)

MI of rod = 1/3*Mr*L^2

= 1/3 x 1.2 kg x (0.71 m)^2

= 0.202 kg m^2

2)

MI of disk = (1/2) Md*R^2

= 1/2 x 3.3 kg x (0.26 m)^2

= 0.112 kg m^2

3)

Total MI = 5* 1/3*Mr*L^2 + (1/2) Md*R^2

= (5 x 1/3 x 1.2 x 0.71^2)+ (1/2 x 3.3 x 0.26^2)

= 1.122 kg m^2

4)

alpha = 2*theta/t^2 = (2*15*2*3.14) / 3.2^2 = 18.3984 rad/s^2

5)

Wf = alpha *t = 58.875 rad/s

6)

KE = 1/2*I*Wf^2

= 0.5 x 1.122 x 58.875^2 =

= 1927.24 J

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