A simplified gear system for a mechanical watch is shown. Know that gear A has a constant angular velocity of 1 rev/h and gear Chas a constant angular velocity of 1 rpm. Given: ch=0.5 in. and d2=0.37 in. d2 B d1 Determine the radius r. (You must provide an answer before moving on to the next part.) The radius r is in.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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**Title: Simplified Gear System for a Mechanical Watch**

**Introduction:**

In this exercise, we'll explore a simplified gear system used in a mechanical watch. The system consists of three gears, labeled as A, B, and C. 

**Description of the System:**

- **Gear A:** This gear has a constant angular velocity of 1 revolution per hour (rev/h).
- **Gear C:** This gear has a constant angular velocity of 1 revolution per minute (rpm).

**Given Parameters:**

- Diameter of gear 1 (\(d_1\)) = 0.5 inches
- Diameter of gear 2 (\(d_2\)) = 0.37 inches

**Diagram Explanation:**

The diagram illustrates the positioning and interconnection of the gears:

- Gear A is the largest, located to the left, and serves as the input gear.
- Gear B is in the middle, slightly smaller than Gear A, and interacts with both Gear A and Gear C.
- Gear C is the smallest, positioned to the right, and serves as the output gear.

The radii of the gears are denoted by \(r\), which you need to determine based on the given diameters and angular velocities.

**Task:**

- Determine the radius \(r\).

**Prompt:**

Fill in the blank below with the appropriate value of \(r\).

The radius \(r\) is _____ in.

Use the given angular velocity and size parameters to calculate the radius accurately. Ensure your answer is precise before proceeding to the next part of this educational module.
Transcribed Image Text:**Title: Simplified Gear System for a Mechanical Watch** **Introduction:** In this exercise, we'll explore a simplified gear system used in a mechanical watch. The system consists of three gears, labeled as A, B, and C. **Description of the System:** - **Gear A:** This gear has a constant angular velocity of 1 revolution per hour (rev/h). - **Gear C:** This gear has a constant angular velocity of 1 revolution per minute (rpm). **Given Parameters:** - Diameter of gear 1 (\(d_1\)) = 0.5 inches - Diameter of gear 2 (\(d_2\)) = 0.37 inches **Diagram Explanation:** The diagram illustrates the positioning and interconnection of the gears: - Gear A is the largest, located to the left, and serves as the input gear. - Gear B is in the middle, slightly smaller than Gear A, and interacts with both Gear A and Gear C. - Gear C is the smallest, positioned to the right, and serves as the output gear. The radii of the gears are denoted by \(r\), which you need to determine based on the given diameters and angular velocities. **Task:** - Determine the radius \(r\). **Prompt:** Fill in the blank below with the appropriate value of \(r\). The radius \(r\) is _____ in. Use the given angular velocity and size parameters to calculate the radius accurately. Ensure your answer is precise before proceeding to the next part of this educational module.
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