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 centripetal force needed to maintain circular motion using angular velocity.

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, grows with the square of angular velocity, and is directly proportional to radius.

3. Importance of Centripetal Force

Details: Understanding centripetal force is crucial for designing rotating systems, amusement park rides, planetary orbits, and particle accelerators.

4. Using the Calculator

Tips: Enter the mass in kg, angular velocity in rad/s (convert from RPM if needed), and radius in meters. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: How is angular velocity different from regular velocity?
A: Angular velocity (ω) measures rotation rate in radians per second, while linear velocity measures straight-line speed in m/s.

Q2: What's the relationship between ω and RPM?
A: ω = RPM × (2π/60). 1 RPM equals approximately 0.1047 rad/s.

Q3: Why does force increase with radius?
A: Larger radius means greater circumference, requiring more force to maintain the same angular velocity.

Q4: What provides centripetal force in different situations?
A: Tension (in a string), friction (for cars turning), gravity (for orbits), or normal force (in rotating devices).

Q5: How does this relate to centrifugal force?
A: Centrifugal force is the apparent outward force in a rotating frame, while centripetal force is the real inward force causing circular motion.