Inner Radius of Circular Ring Given Outer Radius and Longest Interval Calculator

Formula Used:

\[ r_{Inner} = \sqrt{r_{Outer}^2 - \left(\frac{I_{Longest}}{2}\right)^2} \]

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 boundary of the ring.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_{Inner} = \sqrt{r_{Outer}^2 - \left(\frac{I_{Longest}}{2}\right)^2} \]

Where:

\( r_{Inner} \) — Inner Radius of Circular Ring (m)
\( r_{Outer} \) — Outer Radius of Circular Ring (m)
\( I_{Longest} \) — Longest Interval of Circular Ring (m)

Explanation: This formula calculates the inner radius of a circular ring using the Pythagorean theorem, where the longest interval is the chord tangent to the inner circle.

3. Importance of Inner Radius Calculation

Details: Calculating the inner radius is essential in engineering, architecture, and manufacturing for designing rings, washers, pipes, and other circular ring-shaped components with specific dimensions.

4. Using the Calculator

Tips: Enter the outer radius and longest interval in meters. Both values must be positive numbers. The longest interval should be less than or equal to twice the outer radius for a valid result.

5. Frequently Asked Questions (FAQ)

Q1: What is a circular ring?
A: A circular ring is the region between two concentric circles - it has an outer circle and an inner circle with the same center point.

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

Q3: Can this formula be used for any circular ring?
A: Yes, this formula works for any circular ring where you know the outer radius and the longest interval (chord length).

Q4: What if the calculated inner radius is negative?
A: The formula will only produce a real result when the longest interval is less than or equal to twice the outer radius. If the input values don't satisfy this condition, the result will be invalid.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise based on the inputs. The accuracy of the result depends on the accuracy of your measurements for the outer radius and longest interval.