1. What is Angular Velocity?

Definition: Angular velocity measures how fast an object rotates or revolves relative to another point, expressed in radians per second (rad/s).

Purpose: It's essential in physics and engineering for analyzing rotational motion in wheels, gears, turbines, and celestial bodies.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \omega \) — Angular velocity (rad/s)
• \( v \) — Linear velocity (m/s)
• \( r \) — Radius of rotation (m)

Explanation: The linear velocity is divided by the radius to determine how many radians the object rotates through per second.

3. Importance of Angular Velocity

Details: Understanding angular velocity helps in designing mechanical systems, analyzing vehicle dynamics, and studying planetary motion.

4. Using the Calculator

Tips: Enter the linear velocity in m/s and radius in meters. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between angular and linear velocity?
A: Linear velocity measures straight-line speed (m/s), while angular velocity measures rotational speed (rad/s).

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

Q3: Can angular velocity be negative?
A: Yes, negative values indicate rotation in the opposite direction.

Q4: What if my radius is in cm?
A: Convert to meters first (divide cm by 100) before calculation.

Q5: Does this work for any rotating object?
A: Yes, as long as you know the linear velocity at a given radius from the axis of rotation.