1. What is Inner Arc Length of Annulus Sector?

The Inner Arc Length of Annulus Sector is the distance between two points along the inner curve of an annulus sector. An annulus is the region between two concentric circles, and a sector is a portion of this annulus defined by a central angle.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_{\text{outer}} \) — Outer Circle Radius of Annulus (m)
• \( b \) — Breadth of Annulus (m)
• \( \theta \) — Central Angle of Annulus Sector (rad)

Explanation: The inner radius is calculated by subtracting the breadth from the outer radius, and the arc length is then found by multiplying this inner radius by the central angle in radians.

3. Importance of Inner Arc Length Calculation

Details: Calculating the inner arc length of an annulus sector is important in various engineering and geometric applications, particularly in mechanical design, architecture, and manufacturing where annular shapes are common.

4. Using the Calculator

Tips: Enter the outer circle radius and breadth in meters, and the central angle in radians. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is an annulus?
A: An annulus is the region between two concentric circles, resembling a ring or washer shape.

Q2: Why is the central angle measured in radians?
A: Radians are used because they provide a direct relationship between angle and arc length (arc length = radius × angle).

Q3: Can I use degrees instead of radians?
A: The calculator requires radians. To convert degrees to radians, multiply by π/180.

Q4: What if the breadth is larger than the outer radius?
A: The breadth cannot be larger than the outer radius, as this would result in a negative inner radius, which is not physically meaningful.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for the given formula, assuming precise input values.