1. What is Centripetal Acceleration?

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

Purpose: It describes the acceleration needed to maintain circular motion and is essential in physics and engineering applications.

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 centripetal acceleration increases with the square of the angular velocity and linearly with the radius.

3. Importance of Centripetal Acceleration

Details: Understanding centripetal acceleration is crucial for designing circular motion systems, from amusement park rides to satellite orbits.

4. Using the Calculator

Tips: Enter the angular velocity in radians per second and the radius in meters. Both 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 rotation rate in radians/second, while linear velocity (v) is speed along the circular path (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 radius increases but angular velocity stays constant?
A: Centripetal acceleration increases linearly with radius (a_c ∝ r).

Q4: What provides the centripetal force in real-world applications?
A: It can be tension (in a string), friction (for cars turning), gravity (for orbits), or other forces.

Q5: Can centripetal acceleration be negative?
A: No, since it's calculated using ω² (always positive) and radius (positive by definition).