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 physics students and engineers determine the force required to maintain circular motion.

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)

Explanation: The force required to keep an object moving in a circle increases with mass and velocity squared, and decreases with larger radius.

3. Importance of Centripetal Force

Details: Understanding centripetal force is crucial for designing roads, roller coasters, centrifuges, and analyzing planetary motion.

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 real and points inward, while centrifugal force is a fictitious force that appears to push outward in a rotating frame.

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

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

Q4: What happens if centripetal force disappears?
A: The object would move in a straight line (Newton's first law).

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.