A bicycle is turned upside down while its owner repairs a flat tire on the rear wheel. A friend spins the front wheel, of radius 0.383 m, and observes that drops of water fly off tangentially in an upward direction when the drops are at the same level a loose on the next turn rises 51.0 cm above the tangent point. The height to which the drops rise decreases because the angular speed of the wheel decreases. From this information, determine the magnitude of the average angular the center of the wheel. She measures the height reached by drops moving vertically (see figure below). A drop that breaks loose from the tire on one turn rises h = 56.0 cm above the tangent point. A drop that breaks acceleration of the wheel. rad/s?

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### Educational Content on Angular Acceleration

**Problem Statement:**

A bicycle is turned upside down while its owner repairs a flat tire on the rear wheel. A friend spins the front wheel, which has a radius of 0.383 m, and observes that drops of water fly off tangentially in an upward direction when the drops are at the same level as the center of the wheel. The height reached by drops moving vertically is measured.

- **Initial Height (h1):** A drop that breaks loose from the tire on one turn rises to a height \( h = 56.0 \) cm above the tangent point.
- **Subsequent Height (h2):** A drop that breaks loose on the next turn rises to 51.0 cm above the tangent point.

The height to which the drops rise decreases because the angular speed of the wheel decreases. Using this information, determine the magnitude of the average angular acceleration of the wheel.

**Calculation Requirement:**

- **Result Required:** Magnitude of average angular acceleration in rad/s².

**Visualization:**

The image includes a diagram of the bicycle’s front wheel being spun. An arrow indicates the drop being flung off tangentially. The height \( h \) reached by a drop is indicated with a vertical line showing measurement above the tangent point.

**Input:**

- A text box is included for entering the calculated angular acceleration: _______ rad/s². 

This exercise involves applying principles of rotational motion and energy conservation to determine the angular acceleration of the rotating wheel.
Transcribed Image Text:### Educational Content on Angular Acceleration **Problem Statement:** A bicycle is turned upside down while its owner repairs a flat tire on the rear wheel. A friend spins the front wheel, which has a radius of 0.383 m, and observes that drops of water fly off tangentially in an upward direction when the drops are at the same level as the center of the wheel. The height reached by drops moving vertically is measured. - **Initial Height (h1):** A drop that breaks loose from the tire on one turn rises to a height \( h = 56.0 \) cm above the tangent point. - **Subsequent Height (h2):** A drop that breaks loose on the next turn rises to 51.0 cm above the tangent point. The height to which the drops rise decreases because the angular speed of the wheel decreases. Using this information, determine the magnitude of the average angular acceleration of the wheel. **Calculation Requirement:** - **Result Required:** Magnitude of average angular acceleration in rad/s². **Visualization:** The image includes a diagram of the bicycle’s front wheel being spun. An arrow indicates the drop being flung off tangentially. The height \( h \) reached by a drop is indicated with a vertical line showing measurement above the tangent point. **Input:** - A text box is included for entering the calculated angular acceleration: _______ rad/s². This exercise involves applying principles of rotational motion and energy conservation to determine the angular acceleration of the rotating wheel.
Expert Solution
Step 1

Speed of the first drop

vf2=v12-2gh10=v12-2gh1v1=2gh1            1

Similarly, the speed of the second drop is

v2=2gh2            2

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