Diagonal Of Annulus Sector Given Inner Circle Radius And Breadth Of Annulus Calculator

Formula Used:

\[ d_{Sector} = \sqrt{(2 \times r_{Inner} \times (1 - \cos(\angle_{Central(Sector)})) \times (r_{Inner} + b)) + b^2} \]

Diagonal of Annulus Sector:

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1. What is the Diagonal of Annulus Sector?

The Diagonal of Annulus Sector is a line segment joining the two opposite points, at the maximum distance, on the outer and inner arc of an annulus sector. It represents the longest chord that can be drawn across the annular sector.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d_{Sector} = \sqrt{(2 \times r_{Inner} \times (1 - \cos(\angle_{Central(Sector)})) \times (r_{Inner} + b)) + b^2} \]

Where:

\( d_{Sector} \) — Diagonal of Annulus Sector (m)
\( r_{Inner} \) — Inner Circle Radius of Annulus (m)
\( \angle_{Central(Sector)} \) — Central Angle of Annulus Sector (rad)
\( b \) — Breadth of Annulus (m)
\( \cos \) — Cosine trigonometric function
\( \sqrt{} \) — Square root function

Explanation: The formula calculates the diagonal length by considering the geometric properties of the annulus sector, including the inner radius, central angle, and annular breadth.

3. Importance of Diagonal Calculation

Details: Calculating the diagonal of an annulus sector is important in various engineering and architectural applications where precise measurements of annular sections are required, such as in mechanical design, construction, and geometric analysis.

4. Using the Calculator

Tips: Enter the inner circle radius in meters, central angle in radians, and breadth of annulus in meters. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is an annulus sector?
A: An annulus sector is the portion of an annulus (the region between two concentric circles) bounded by two radii and their intercepted arcs.

Q2: Why is the cosine function used in this formula?
A: The cosine function helps calculate the chord length component of the diagonal based on the central angle of the sector.

Q3: Can this calculator handle degrees instead of radians?
A: The calculator requires input in radians. To convert degrees to radians, multiply degrees by π/180.

Q4: What is the significance of the square root in the formula?
A: The square root calculates the final diagonal length from the squared sum of the chord component and the breadth squared.

Q5: Are there any limitations to this calculation?
A: The formula assumes perfect circular geometry and may not account for irregularities or deformations in real-world annular shapes.