1. What is Centripetal Force?

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

Purpose: This calculator helps determine the force required to maintain circular motion based on the object's mass, angular velocity, and radius of rotation.

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 the square of angular velocity and linearly with both mass and radius.

3. Importance of Centripetal Force

Details: Understanding centripetal force is crucial in designing rotating machinery, amusement park rides, planetary orbits, and many engineering applications.

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 rotational speed in radians per second, while linear velocity (v) measures straight-line speed in m/s (v = ω × r).

Q2: What's the difference between centripetal and centrifugal force?
A: Centripetal force is real and acts inward, while centrifugal force is a fictitious apparent force that seems to push outward in a rotating frame.

Q3: How do I convert RPM to rad/s?
A: Multiply RPM by 2π/60 (e.g., 60 RPM = 60 × 0.10472 ≈ 6.283 rad/s).

Q4: What are some real-world examples?
A: Car turning (friction provides F_c), planets orbiting (gravity provides F_c), spinning a ball on a string (tension provides F_c).

Q5: What if I know linear velocity instead of angular?
A: Use the alternative formula: F_c = m × v²/r where v is linear velocity.