Central Angle Of Annulus Sector Given Diagonal And Inner Circle Radius Calculator

Formula Used:

\[ \text{Central Angle of Annulus Sector} = \cos^{-1}\left(1-\frac{(\text{Diagonal of Annulus Sector}^2-\text{Breadth of Annulus}^2)}{2\times\text{Inner Circle Radius of Annulus}\times(\text{Inner Circle Radius of Annulus}+\text{Breadth of Annulus})}\right) \]

Central Angle of Annulus Sector:

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1. What is the Central Angle of Annulus Sector?

The Central Angle of Annulus Sector is the angle whose apex (vertex) is the center of the concentric circles of Annulus and whose legs (sides) are radii intersecting the circles in four distinct points.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Central Angle} = \cos^{-1}\left(1-\frac{(d_{Sector}^2-b^2)}{2\times r_{Inner}\times(r_{Inner}+b)}\right) \]

Where:

\( d_{Sector} \) — Diagonal of Annulus Sector (m)
\( b \) — Breadth of Annulus (m)
\( r_{Inner} \) — Inner Circle Radius of Annulus (m)

Explanation: The formula calculates the central angle by considering the geometric relationship between the diagonal, breadth, and inner radius of the annulus sector.

3. Importance of Central Angle Calculation

Details: Calculating the central angle is essential for determining the area and perimeter of annulus sectors, which has applications in engineering, architecture, and various geometric calculations.

4. Using the Calculator

Tips: Enter diagonal of annulus sector, breadth of annulus, and inner circle radius in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

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

Q2: How is this different from a regular circle sector?
A: While a circle sector is from a single circle, an annulus sector involves two concentric circles, creating a ring-shaped sector.

Q3: What are practical applications of this calculation?
A: This calculation is used in mechanical engineering for gear design, in architecture for circular structures, and in various manufacturing processes involving circular components.

Q4: Can this formula be used for any annulus sector?
A: Yes, the formula works for any annulus sector where the diagonal, breadth, and inner radius are known and the geometric constraints are satisfied.

Q5: What units should be used for input values?
A: The calculator uses meters as the default unit, but any consistent unit system can be used as long as all inputs are in the same units.