1. What is Angular Velocity?

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

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 (radians/second)
• \( v \) — Linear velocity (meters/second)
• \( r \) — Radius of rotation (meters)

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 the 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 angular velocity to RPM?
A: Multiply ω by 60/(2π) ≈ 9.549 to get revolutions per minute (RPM).

Q3: What if my radius is in centimeters?
A: Convert to meters first (divide by 100) before using the calculator.

Q4: Can angular velocity be negative?
A: Yes, negative values indicate rotation in the opposite direction.

Q5: What's a typical angular velocity for a car wheel?
A: At 60 mph (26.8 m/s) with 0.3m radius tires, ω ≈ 89.3 rad/s or about 853 RPM.