1. What is Centripetal Force?

Definition: Centripetal force is the net force required to keep an object moving in a circular path at constant speed.

Purpose: This calculator helps determine the inward force needed for circular motion, important in physics, engineering, and various applications like roller coasters, planetary orbits, and centrifuges.

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 increases with mass and the square of velocity, but decreases with larger radius.

3. Importance of Centripetal Force

Details: Understanding centripetal force is crucial for designing safe curves in roads, calculating satellite orbits, and analyzing particle motion in accelerators.

4. Using the Calculator

Tips: Enter the mass in kg, velocity in m/s, and radius in meters. All values must be positive (radius 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 causing circular motion. Centrifugal is the apparent outward force in a rotating frame.

Q2: What happens if centripetal force disappears?
A: The object would move in a straight line (Newton's first law).

Q3: How does this relate to angular velocity?
A: The formula can also be written as \( F_c = m \times \omega^2 \times r \) where ω is angular velocity.

Q4: What provides centripetal force in different situations?
A: Tension (in a string), friction (for cars turning), gravity (for orbits), or normal force (on roller coasters).

Q5: Why is velocity squared in the formula?
A: Because kinetic energy (and thus required force) increases with the square of velocity.