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 2.80 kg and radius 0.200 m. Each rod has mass 0.850 kg and is 0.760 m long.

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## Ceiling Fan Dynamics

### Problem Description

An approximate model for a ceiling fan consists of a cylindrical disk with four thin rods extending from the disk's center, as shown in the figure below. The disk has a mass of 2.80 kg and a radius of 0.200 m. Each rod has a mass of 0.850 kg and is 0.760 m long.

**Figure:**
![Ceiling Fan Diagram](image-link)
[Description: The figure shows a central cylindrical disk with four elongated rods extending from the disk's center.]

### Questions

**(a)** Find the ceiling fan's moment of inertia about a vertical axis through the disk's center. (Enter your answer in kg·m².)

Input Box:
```
____________________________________ kg·m²
```

**(b)** Friction exerts a constant torque of magnitude 0.113 N·m on the fan as it rotates. Calculate 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 N·m.)

Input Box:
```
____________________________________ N·m
```

### Figure Explanation

The provided figure illustrates the ceiling fan model used for the calculations. It shows:
- A central cylindrical disk.
- Four thin rods extending outward from the disk's center. 

Each component's mass and dimensions are given, enabling the calculation of the fan's moment of inertia and the necessary torque provided by the motor to overcome friction and achieve maximum speed.
Transcribed Image Text:## Ceiling Fan Dynamics ### Problem Description An approximate model for a ceiling fan consists of a cylindrical disk with four thin rods extending from the disk's center, as shown in the figure below. The disk has a mass of 2.80 kg and a radius of 0.200 m. Each rod has a mass of 0.850 kg and is 0.760 m long. **Figure:** ![Ceiling Fan Diagram](image-link) [Description: The figure shows a central cylindrical disk with four elongated rods extending from the disk's center.] ### Questions **(a)** Find the ceiling fan's moment of inertia about a vertical axis through the disk's center. (Enter your answer in kg·m².) Input Box: ``` ____________________________________ kg·m² ``` **(b)** Friction exerts a constant torque of magnitude 0.113 N·m on the fan as it rotates. Calculate 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 N·m.) Input Box: ``` ____________________________________ N·m ``` ### Figure Explanation The provided figure illustrates the ceiling fan model used for the calculations. It shows: - A central cylindrical disk. - Four thin rods extending outward from the disk's center. Each component's mass and dimensions are given, enabling the calculation of the fan's moment of inertia and the necessary torque provided by the motor to overcome friction and achieve maximum speed.
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