A ceiling fan consists of a small cylindrical disk with 5 thin rods coming from
ID: 1286501 • Letter: A
Question
A ceiling fan consists of a small cylindrical disk with 5 thin rods coming from the center. The disk has mass md = 3.1 kg and radius R = 0.24 m. The rods each have mass mr = 1.3 kg and length L = 0.78 m.
1)What is the moment of inertia of each rod about the axis of rotation?
2)What is the moment of inertia of the disk about the axis of rotation?
3)What is the moment of inertia of the whole ceiling fan?
4)When the fan is turned on, it takes t = 3.2 s and a total of 13 revolutions to accelerate up to its full speed.
What is the magnitude of the angular acceleration?
5)What is the final angular speed of the fan?
6)What is the final rotational energy of the fan?
What is the final angular speed of the fan?
8)What is the magnitude of the angular acceleration while the fan slows down?
A ceiling fan consists of a small cylindrical disk with 5 thin rods coming from the center. The disk has mass md = 3.1 kg and radius R = 0.24 m. The rods each have mass mr = 1.3 kg and length L = 0.78 m. 1)What is the moment of inertia of each rod about the axis of rotation? 2)What is the moment of inertia of the disk about the axis of rotation? 3)What is the moment of inertia of the whole ceiling fan? 4)When the fan is turned on, it takes t = 3.2 s and a total of 13 revolutions to accelerate up to its full speed. What is the magnitude of the angular acceleration? 5)What is the final angular speed of the fan? 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 arrow-10x10.pngto this new speed is also t = 3.2 s. What is the final angular speed of the fan? 8)What is the magnitude of the angular acceleration while the fan slows down?Explanation / Answer
When the fan is turned on, it takes t = 3.3 s and a total of 18 revolutions to accelerate up to its full speed. What is the magnitude of angular acceleration?
18*2*pi= 0.5*alpha*3.3^2 or angular acceleration alpha = 72*pi/(3.3^2) = 20.77 rad/s^2
What I've found:
Moment of Inertia for each rod: . [{1.3*(0.87^2)*(1/24)}= 0.041, your answer is wrong formula is (ML^2 /24)
Moment of Inertia of the disk: .08228(0.5*3.2*0.22^2= 0.08228, you are right!
Moment of Inertia for the whole fan: [0.041*5+0.08228] = 1.03 kg m^2
Also:
The final angular speed of the fan? = 20.77*3.3 = 68.54 rad/s
The final rotational energy of the fan = 0.5*I*68.54^2 = 2414 J
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 = 3.3 s. What is the final angular speed of the fan
Energy in second setting = 2414/2 = 1207 = 0.5*1.02*omega^2 or
reduced angular velocity, omega = sq rt[(1207*2)/1.02] = 48.65 rad/s
The magnitude of the angular acceleration while the fan slows down = (68.54-48.65)/3.3 = 6.03 rad/s^2
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