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 needed to maintain circular motion for a given 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)
• \( v \) — Tangential velocity (meters/second)
• \( r \) — Radius of circular path (meters)

Explanation: The force required increases with mass and the square of velocity, but decreases with larger radius.

3. Importance of Centripetal Force

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

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 inward force, while centrifugal force is the apparent outward force in a rotating frame.

Q2: How does velocity affect centripetal force?
A: Force increases with the square of velocity - doubling speed requires 4× the force.

Q3: What are real-world examples of centripetal force?
A: Car turning (friction provides force), Earth's orbit (gravity), spinning ball on string (tension).

Q4: What happens if centripetal force disappears?
A: The object would move in a straight line tangent to its previous circular path.

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