1. What is Centripetal Force?

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

Purpose: This calculator helps determine the required centripetal force based on an 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, 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 required to maintain circular motion increases with mass, grows with the square of angular velocity, and is directly proportional to radius.

3. Importance of Centripetal Force Calculation

Details: Understanding centripetal force is crucial in designing rotating machinery, amusement park rides, vehicle dynamics, and orbital mechanics.

4. Using the Calculator

Tips: Enter the mass in kg, angular velocity in rad/s, and radius in m. 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. They're related by v = ωr.

Q2: What's the difference between centripetal and centrifugal force?
A: Centripetal force is the real inward force causing circular motion. Centrifugal force is a fictitious outward force apparent in rotating reference frames.

Q3: How do I convert RPM to rad/s?
A: Multiply RPM by 2π/60. For example, 60 RPM = 60 × (2π/60) = 6.28 rad/s.

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

Q5: Can this formula be used for planetary orbits?
A: Yes, but gravitational force provides the centripetal force in that case (F_g = F_c).