Inner Radius of Circular Ring given Longest Interval and Perimeter Calculator

Formula Used:

\[ r_{Inner} = \frac{\left(\frac{P}{2\pi}\right) - \left(\frac{\frac{I_{Longest}^2}{4}}{\frac{P}{2\pi}}\right)}{2} \]

Inner Radius of Circular Ring:

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1. What is the Inner Radius of Circular Ring?

The Inner Radius of Circular Ring is the radius of its cavity and the smaller radius among two concentric circles that form the circular ring.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_{Inner} = \frac{\left(\frac{P}{2\pi}\right) - \left(\frac{\frac{I_{Longest}^2}{4}}{\frac{P}{2\pi}}\right)}{2} \]

Where:

\( r_{Inner} \) — Inner Radius of Circular Ring (m)
\( P \) — Perimeter of Circular Ring (m)
\( I_{Longest} \) — Longest Interval of Circular Ring (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula calculates the inner radius based on the perimeter of the circular ring and its longest chord length.

3. Importance of Inner Radius Calculation

Details: Calculating the inner radius is important in various engineering and geometric applications where circular rings are used, such as in mechanical design, architecture, and manufacturing.

4. Using the Calculator

Tips: Enter the perimeter and longest interval values in meters. Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a circular ring?
A: A circular ring is the region between two concentric circles, consisting of an outer circle and an inner circle.

Q2: What is the longest interval of a circular ring?
A: The longest interval is the length of the longest chord that can be drawn within the circular ring, which is tangent to the inner circle.

Q3: Can this formula be used for elliptical rings?
A: No, this formula is specifically designed for circular rings with concentric circles.

Q4: What are typical applications of circular rings?
A: Circular rings are commonly used in pipe systems, washers, bearings, and various mechanical components.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise when the input values are accurate and the ring is perfectly circular.