1. What is the Linear Velocity and Angular Velocity Relationship?

Definition: This calculator determines the linear velocity of a point moving in a circular path based on its angular velocity and radius.

Purpose: It helps in physics, engineering, and mechanical applications where rotational motion needs to be converted to linear motion.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( V \) — Linear velocity (meters/second)
• \( \omega \) — Angular velocity (radians/second)
• \( r \) — Radius of rotation (meters)

Explanation: The linear velocity of a point on a rotating object equals the product of its angular velocity and the distance from the rotation axis.

3. Importance of Velocity Conversion

Details: Understanding this relationship is crucial for designing rotating machinery, analyzing circular motion, and converting between rotational and linear measurements.

4. Using the Calculator

Tips: Enter the angular velocity in radians/second and the radius in meters. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: How do I convert RPM to rad/s?
A: Multiply RPM by 2π/60 (e.g., 60 RPM = 60 × 2π/60 ≈ 6.283 rad/s).

Q2: Does this formula work for any point on a rotating object?
A: Yes, but remember that r is the distance from the rotation axis to the specific point.

Q3: What if I know linear velocity and need angular velocity?
A: Rearrange the formula: ω = V/r.

Q4: Are there limitations to this formula?
A: It assumes rigid body rotation and doesn't account for relativistic effects at extremely high speeds.

Q5: How is this used in real-world applications?
A: Common in designing gears, wheels, turbines, and any system converting between rotational and linear motion.