1. What is Uniform Circular Motion?

Uniform circular motion describes the motion of an object traveling at constant speed along a circular path. The net force causing this motion is called centripetal force, directed toward the center of the circular path.

2. How Does the Calculator Work?

The calculator uses the centripetal force formula:

Where:

• \( F \) — Centripetal force (N)
• \( m \) — Mass of the object (kg)
• \( \omega \) — Angular velocity (rad/s)
• \( r \) — Radius of the circular path (m)

Explanation: The equation shows that centripetal force increases with mass, grows with the square of angular velocity, and is directly proportional to radius.

3. Importance of Centripetal Force

Details: Centripetal force is essential for understanding circular motion in physics, engineering applications like roller coasters, planetary orbits, and particle accelerators.

4. Using the Calculator

Tips: Enter mass in kilograms, angular velocity in radians per second, and radius in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between angular velocity and linear velocity?
A: Angular velocity (ω) measures rotational speed in radians per second, while linear velocity (v) is the tangential speed in m/s, related by v = ωr.

Q2: How does this relate to centrifugal force?
A: Centrifugal force is a fictitious force that appears in rotating reference frames, while centripetal force is the real inward force causing circular motion.

Q3: What happens if centripetal force is removed?
A: The object will move in a straight line tangent to the circle (Newton's first law).

Q4: Can this formula be used for planetary motion?
A: Yes, with gravity providing the centripetal force, though relativistic effects become significant for extreme cases.

Q5: How is this applied in real-world engineering?
A: Used in designing roads, roller coasters, centrifuges, and any system involving circular motion.