1. What is Centripetal Acceleration (Angular)?

Definition: Centripetal acceleration is the acceleration directed toward the center of a circular path that keeps an object moving along that path.

Purpose: This calculator helps determine the centripetal acceleration when the angular velocity and radius of the circular motion are known.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( a_c \) — Centripetal acceleration (m/s²)
• \( \omega \) — Angular velocity (radians/second)
• \( r \) — Radius of circular path (meters)

Explanation: The angular velocity is squared and multiplied by the radius to calculate the centripetal acceleration.

3. Importance of Centripetal Acceleration

Details: Understanding centripetal acceleration is crucial in designing circular motion systems like rotors, centrifuges, and orbital mechanics.

4. Using the Calculator

Tips: Enter the angular velocity in radians per second and the radius in meters. All values must be > 0.

5. Frequently Asked Questions (FAQ)

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

Q2: How do I convert RPM to rad/s?
A: Multiply RPM by 2π/60 (e.g., 60 RPM = 6.283 rad/s).

Q3: Does this work for any circular motion?
A: Yes, as long as the angular velocity is constant (uniform circular motion).

Q4: What's the relationship to centripetal force?
A: Centripetal force = mass × centripetal acceleration (F = ma_c).

Q5: Can I use this for planetary orbits?
A: Yes, though gravitational forces would need to be considered for complete orbital calculations.