1. What is Circular Velocity?

Circular velocity is the velocity needed for an object to maintain circular motion at a given radius under a specific gravitational acceleration. It's fundamental in orbital mechanics and circular motion physics.

2. How Does the Calculator Work?

The calculator uses the circular velocity equation:

Where:

• \( v \) — Circular velocity (m/s)
• \( g \) — Gravitational acceleration (m/s²)
• \( r \) — Radius of circular path (m)

Explanation: The equation shows that velocity increases with both gravitational acceleration and radius of the circular path.

3. Importance of Circular Velocity

Details: Circular velocity calculations are essential for satellite orbit design, amusement park ride safety, and understanding planetary motion in astronomy.

4. Using the Calculator

Tips: Enter gravitational acceleration in m/s² (9.81 m/s² on Earth's surface) and radius in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between circular and orbital velocity?
A: Circular velocity is for surface-level circular motion, while orbital velocity accounts for altitude above the central body.

Q2: How does circular velocity relate to centripetal force?
A: Centripetal force (F = mv²/r) maintains circular motion at this velocity.

Q3: What happens if velocity is less than circular velocity?
A: The object will spiral inward, unable to maintain the circular path.

Q4: Can this be used for planetary orbits?
A: For planetary orbits, use \( v = \sqrt{GM/r} \) where G is gravitational constant and M is central mass.

Q5: What are typical circular velocity values?
A: On Earth's surface (r≈6.371×10⁶ m), circular velocity is about 7.9 km/s (first cosmic velocity).