1. What is Height of Cycloid?

The Height of Cycloid formula is defined as the measure of vertical distance from one top to bottom face of Cycloid. A cycloid is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line without slipping.

2. How Does the Calculator Work?

The calculator uses the Height of Cycloid formula:

Where:

• \( h \) — Height of Cycloid (m)
• \( l_{Arc} \) — Arc Length of Cycloid (m)

Explanation: The height of a cycloid is exactly one-fourth of its arc length, making this a simple and elegant mathematical relationship.

3. Importance of Height Calculation

Details: Calculating the height of a cycloid is important in various fields including physics, engineering, and mathematics, particularly in the study of curves and motion of rolling objects.

4. Using the Calculator

Tips: Enter the arc length of the cycloid in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a cycloid?
A: A cycloid is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line without slipping.

Q2: Why is the height exactly one-fourth of the arc length?
A: This is a fundamental property of cycloids derived from their geometric construction and parametric equations.

Q3: Can this formula be used for any cycloid?
A: Yes, this relationship holds true for all standard cycloids where the generating circle rolls along a straight line.

Q4: What are the practical applications of cycloids?
A: Cycloids have applications in gear design, pendulum clocks (cycloidal pendulum), and various mechanical systems.

Q5: How is arc length of cycloid calculated?
A: The arc length of a complete cycloid arch is 8 times the radius of the generating circle: \( l_{Arc} = 8r \).