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 inward force required to maintain circular motion for a given mass, velocity, and radius.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( F \) — Centripetal force (Newtons, N)
• \( m \) — Mass of the object (kilograms, kg)
• \( v \) — Velocity of the object (meters per second, m/s)
• \( r \) — Radius of the circular path (meters, m)

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 roads, roller coasters, and any system involving circular 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 is the real inward force, while centrifugal is the apparent outward force felt in a rotating reference frame.

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

Q3: What are some real-world examples?
A: Car turning a corner, planets orbiting the sun, or a ball on a string being swung in a circle.

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: How is this related to angular velocity?
A: For objects rotating at ω radians/second, v = rω, so F = mω²r.