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 force required to maintain circular motion based on mass, velocity, and radius.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( F_c \) — Centripetal force (Newtons)
• \( m \) — Mass of the object (kilograms)
• \( v \) — Velocity of the object (meters/second)
• \( r \) — Radius of the circular path (meters)

Derivation: Starting from Newton's second law \( F = ma \) and the centripetal acceleration \( a = \frac{v^2}{r} \), we substitute to get \( F_c = m \frac{v^2}{r} \).

3. Importance of Centripetal Force

Details: Understanding centripetal force is crucial in designing circular motion systems like roller coasters, planetary orbits, and centrifuges.

4. Using the Calculator

Tips: Enter the mass in kg, velocity in m/s, and radius in m. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between centripetal and centrifugal force?
A: Centripetal force is the real force directed towards the center, while centrifugal force is a fictitious force that appears to act outward in a rotating frame of reference.

Q2: What are some real-world examples?
A: Car turning on a curve (friction provides centripetal force), Earth's orbit around the Sun (gravity provides centripetal force), spinning a ball on a string.

Q3: How does radius affect the force?
A: Force is inversely proportional to radius - smaller circles require more force for the same speed.

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

Q5: How is this related to angular velocity?
A: The formula can also be written as \( F_c = m \omega^2 r \) where \( \omega \) is angular velocity in radians/second.