1. What is Centripetal Force?

Definition: Centripetal force is the force that keeps an object moving in a circular path, directed toward the center of rotation.

Purpose: This calculator determines the force required to maintain circular motion based on mass, angular velocity, and radius.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( F \) — Centripetal force (Newtons, N)
• \( m \) — Mass of the object (kilograms, kg)
• \( \omega \) — Angular velocity (radians per second, rad/s)
• \( r \) — Radius of circular path (meters, m)

Explanation: The force increases with mass, with the square of angular velocity, and linearly with radius.

3. Importance of Centripetal Force

Details: Understanding centripetal force is crucial in designing rotating machinery, amusement park rides, and analyzing planetary motion.

4. Using the Calculator

Tips: Enter the mass in kg, angular velocity in rad/s, and radius in m. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: How is angular velocity different from regular velocity?
A: Angular velocity measures rotation rate (angle per time) while linear velocity measures distance per time.

Q2: What happens if the force is insufficient?
A: The object will move in a larger radius or break from circular motion (centrifugal effect).

Q3: How do I convert RPM to rad/s?
A: Multiply RPM by π/30 (e.g., 60 RPM × π/30 ≈ 6.28 rad/s).

Q4: Does this apply to planetary orbits?
A: Yes, gravity provides the centripetal force for planetary motion.

Q5: What's the difference between centripetal and centrifugal force?
A: Centripetal is real inward force, centrifugal is apparent outward force in rotating frames.