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 determines the inward force needed for circular motion when angular velocity is known.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( F_c \) — Centripetal force (Newtons)
• \( m \) — Mass of the object (kilograms)
• \( \omega \) — Angular velocity (radians per second)
• \( r \) — Radius of circular path (meters)

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 systems, analyzing planetary motion, and engineering applications like centrifuges and roller coasters.

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 (v) measures straight-line speed in m/s. They're related by v = ωr.

Q2: 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 felt in a rotating frame.

Q3: How do I convert RPM to rad/s?
A: Multiply RPM by 2π/60. Example: 60 RPM = 6.283 rad/s.

Q4: Does this formula work for planetary orbits?
A: Yes, it applies to any circular motion, including orbits where gravity provides the centripetal force.

Q5: What if my motion isn't perfectly circular?
A: For elliptical paths, the formula gives instantaneous force at each point based on local radius and speed.