1. What is Centripetal Force?

Centripetal force is the force that keeps an object moving in a circular path, directed towards the center around which the object is moving. It's not a separate force but rather the name given to whatever force is causing the circular motion.

2. Understanding the Formula

The centripetal force formula is:

Where:

• \( F \) — Centripetal force (newtons)
• \( m \) — Mass of the object (kilograms)
• \( v \) — Velocity of the object (meters per second)
• \( r \) — Radius of the circular path (meters)

Explanation: The force required to keep an object moving in a circle increases with the square of the velocity, directly with mass, and decreases with increasing radius.

3. Practical Applications

Examples: This formula is used in designing roller coasters, calculating forces on planets in orbit, determining proper banking angles for roads, and analyzing particle accelerators.

4. How to Use This Calculator

Instructions: Enter the mass in kilograms, velocity in meters per second, and radius in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Is centripetal force a real force?
A: Centripetal force is a name we give to whatever net force is causing circular motion, whether it's tension, gravity, friction, or another force.

Q2: What's the difference between centripetal and centrifugal force?
A: Centripetal force is real and directed inward, while centrifugal force is a fictitious force that appears to act outward in a rotating frame of reference.

Q3: Why does the formula have velocity squared?
A: Because kinetic energy increases with the square of velocity, and more energy requires more force to maintain the circular path.

Q4: What happens if centripetal force disappears?
A: The object will move in a straight line tangent to its former circular path (Newton's first law).

Q5: Can this formula be used for planetary orbits?
A: Yes, gravity provides the centripetal force that keeps planets in orbit around the sun.