Question 2 of 2 Axis Your answer is partially correct. Number The drawing shows the top view of two doors. The doors are uniform and identical. Door A rotates about an axis through its left edge, and door B rotates about an axis through its center. The same force is applied perpendicular to each door at its right edge, and the force remains perpendicular as the door turns. No other force affects the rotation of either door. Starting from rest, door A rotates through a certain angle in 3.00 s. How long does it take door B (also starting from rest) to rotate through the same angle? Door A < Axis Door B Touthook and Media ! Units 0.1/1 S E :

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### Problem Description:

The drawing shows the top view of two doors. The doors are uniform and identical. Door A rotates about an axis through its left edge, and door B rotates about an axis through its center. The same force is applied perpendicular to each door at its right edge, and the force remains perpendicular as the door turns. No other force affects the rotation of either door. Starting from rest, door A rotates through a certain angle in 3.00 s. How long does it take door B (also starting from rest) to rotate through the same angle?

#### Diagram Explanation:

- **Diagram Details:**
  - **Door A:**
    - **Axis:** Positioned at the left edge of Door A.
    - **Force (F):** Applied perpendicular to the right edge of Door A.
  - **Door B:**
    - **Axis:** Positioned through the center of Door B.
    - **Force (F):** Applied perpendicular to the right edge of Door B.

The diagram visually represents the two different scenarios showing the placement of the force and the axis of rotation for both doors.

### Solving the Problem:

1. **Understanding Rotational Motion:**
   - When a force is applied at a certain distance from the axis of rotation, it creates a torque which causes rotational motion.
   - Torque (τ) = Force (F) * Distance from the axis (r)

2. **Comparison of Doors A and B:**
   - For Door A, the force is applied at a distance \( r \) from the left edge.
   - For Door B, the force is applied at a distance \( r/2 \) from the center (since Door B's axis is centered).

3. **Moment of Inertia:**
   - For identical, uniform doors:
     - Moment of inertia of Door A (I_A) about its edge \( = \frac{1}{3} mL^2 \)
     - Moment of inertia of Door B (I_B) about its center \( = \frac{1}{12} mL^2 \)

4. **Angular Acceleration:**
   - Angular acceleration (α) is given by \( α = \frac{Torque}{Moment \ of \ Inertia} \).

5. **Calculations:**
   - Door A: 
     \( τ_A = F * L \)
     \( I_A = \frac{1}{3} mL^2
Transcribed Image Text:### Problem Description: The drawing shows the top view of two doors. The doors are uniform and identical. Door A rotates about an axis through its left edge, and door B rotates about an axis through its center. The same force is applied perpendicular to each door at its right edge, and the force remains perpendicular as the door turns. No other force affects the rotation of either door. Starting from rest, door A rotates through a certain angle in 3.00 s. How long does it take door B (also starting from rest) to rotate through the same angle? #### Diagram Explanation: - **Diagram Details:** - **Door A:** - **Axis:** Positioned at the left edge of Door A. - **Force (F):** Applied perpendicular to the right edge of Door A. - **Door B:** - **Axis:** Positioned through the center of Door B. - **Force (F):** Applied perpendicular to the right edge of Door B. The diagram visually represents the two different scenarios showing the placement of the force and the axis of rotation for both doors. ### Solving the Problem: 1. **Understanding Rotational Motion:** - When a force is applied at a certain distance from the axis of rotation, it creates a torque which causes rotational motion. - Torque (τ) = Force (F) * Distance from the axis (r) 2. **Comparison of Doors A and B:** - For Door A, the force is applied at a distance \( r \) from the left edge. - For Door B, the force is applied at a distance \( r/2 \) from the center (since Door B's axis is centered). 3. **Moment of Inertia:** - For identical, uniform doors: - Moment of inertia of Door A (I_A) about its edge \( = \frac{1}{3} mL^2 \) - Moment of inertia of Door B (I_B) about its center \( = \frac{1}{12} mL^2 \) 4. **Angular Acceleration:** - Angular acceleration (α) is given by \( α = \frac{Torque}{Moment \ of \ Inertia} \). 5. **Calculations:** - Door A: \( τ_A = F * L \) \( I_A = \frac{1}{3} mL^2
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