1. What is Centripetal Force?

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

Purpose: This calculator helps determine the force needed to maintain 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 per 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. Practical Applications

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 happens when velocity doubles?
A: The force increases by a factor of four, since force depends on velocity squared.

Q2: Is this the same as centrifugal force?
A: No, centrifugal force is a fictitious force that appears in rotating reference frames.

Q3: What units should I use?
A: Use kilograms for mass, meters/second for velocity, and meters for radius to get Newtons.

Q4: Can this be used for vertical circular motion?
A: For vertical motion, you must also account for gravity's effect.

Q5: What's a typical value for car turning?
A: A 1000kg car at 20m/s (45mph) in a 50m radius curve experiences about 8000N of centripetal force.