1. What is Centripetal Force?

Definition: Centripetal force is the net force required to keep an object moving in a circular path at constant speed.

Purpose: This calculator determines the inward force needed for circular motion based on mass, velocity, and radius.

2. How Does the Formula Work?

The calculator uses the formula:

Where:

• \( F \) — Centripetal force (Newtons, N)
• \( m \) — Mass of the object (kilograms, kg)
• \( v \) — Tangential velocity (meters/second, m/s)
• \( r \) — Radius of circular path (meters, m)

Explanation: The force increases with mass and the square of velocity, but decreases with larger radius.

3. Applications of Centripetal Force

Examples: Calculating forces for:

• Planetary orbits
• Amusement park rides
• Vehicle turning on curves
• Atomic particles in cyclotrons

4. Using the Calculator

Tips: Enter mass (kg), velocity (m/s), and radius (m). All values must be positive (radius > 0).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between centripetal and centrifugal force?
A: Centripetal is the real inward force causing circular motion. Centrifugal is the apparent outward force in a rotating frame.

Q2: What happens when velocity increases?
A: Force increases with the square of velocity - double speed means 4× the force needed.

Q3: Why does radius appear in the denominator?
A: Larger circles require less force to maintain the same speed (gentler curves).

Q4: What units should I use?
A: Use kg for mass, m/s for velocity, and m for radius to get Newtons (N).

Q5: Can this be used for vertical circular motion?
A: For vertical motion, you must also account for gravity's changing effect.