1. What is Centripetal Force With Angular Velocity?

Definition: This calculator computes the centripetal force required to keep an object moving in a circular path based on its mass, angular velocity, and radius of rotation.

Purpose: It helps physicists, engineers, and students determine the inward force needed for circular motion when angular velocity is known.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( F_c \) — Centripetal force (Newtons, N)
• \( m \) — Mass of the object (kilograms, kg)
• \( \omega \) — Angular velocity (radians per second, rad/s)
• \( r \) — Radius of circular path (meters, m)

Explanation: The mass is multiplied by the square of angular velocity and the radius to determine the required inward force.

3. Importance of Centripetal Force Calculation

Details: Proper calculation ensures safety in rotating systems, helps design mechanical components, and explains circular motion in physics.

4. Using the Calculator

Tips: Enter the mass in kg, angular velocity in rad/s, and radius in m. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between angular velocity and linear velocity?
A: Angular velocity (ω) measures rotation rate in radians per second, while linear velocity (v) measures straight-line speed in m/s. They're related by v = ωr.

Q2: How do I convert RPM to rad/s?
A: Multiply RPM by 2π/60 (1 RPM = 0.10472 rad/s).

Q3: What happens if centripetal force is insufficient?
A: The object will move outward (following inertia) rather than maintaining circular motion.

Q4: Can this formula be used for planetary motion?
A: Yes, it's fundamental to orbital mechanics, though gravitational force provides the centripetal force in that case.

Q5: Why does the force depend on ω²?
A: Because both the velocity and the rate of direction change increase with ω, requiring more force to maintain circular motion.