A ceiling fan consists of a small cylindrical disk with 5 thin rods coming from the center. The disk has mass m_d = 2.9 kg and radius R = 0.22 m. The rods each have mass m_r = 1.4 kg and length L = 0.81 m.

1)What is the moment of inertia of each rod about the axis of rotation? kg-m²

2)What is the moment of inertia of the disk about the axis of rotation? kg-m²

3)What is the moment of inertia of the whole ceiling fan? kg-m²

4)When the fan is turned on, it takes t = 3.2 s and a total of 17 revolutions to accelerate up to its full speed.

What is the magnitude of the angular acceleration? rad/s²

5)What is the final angular speed of the fan? rad/s

6)What is the final rotational energy of the fan? J

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 = 3.2 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/s²

A disk with mass m = 9.7 kg and radius R = 0.31 m begins at rest and accelerates uniformly for t = 18.5 s, to a final angular speed of = 30 rad/s.

1)What is the angular acceleration of the disk? rad/s²

2)What is the angular displacement over the 18.5 s? rad

3)What is the moment of inertia of the disk? kg-m²

4)What is the change in rotational energy of the disk? J

5)What is the tangential component of the acceleration of a point on the rim of the disk when the disk has accelerated to half its final angular speed? m/s²

6)What is the magnitude of the radial component of the acceleration of a point on the rim of the disk when the disk has accelerated to half its final angular speed? m/s²

7)What is the final speed of a point on the disk half-way between the center of the disk and the rim? m/s

8)What is the total distance a point on the rim of the disk travels during the 18.5 seconds? m