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 determines the centripetal force required to keep an object of given mass moving at a specific velocity along a circular path of given radius.

2. How Does the Formula Work?

The calculator uses the formula:

Where:

• \( F_c \) — 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 to maintain circular motion increases with the square of velocity and decreases with increasing radius.

3. Practical Applications

Examples: Calculating forces in amusement park rides, vehicle turning dynamics, planetary orbits, and particle accelerators.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between centripetal and centrifugal force?
A: Centripetal force is the real force directed toward the center, while centrifugal force is the apparent outward force felt in a rotating frame of reference.

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

Q3: What happens if the radius becomes very large?
A: The required centripetal force decreases, approaching straight-line motion as radius approaches infinity.

Q4: Can this formula be used for planetary motion?
A: Yes, it describes the gravitational force needed to maintain a planet's orbit around a star.

Q5: What are common sources of centripetal force?
A: Tension (in a string), friction (for vehicles), gravity (for orbits), or normal force (in rotating systems).