1. What is Angular Velocity?

Definition: Angular velocity is the rate of change of angular displacement with respect to time.

Purpose: It measures how fast an object rotates or revolves relative to another point.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \omega \) — Angular velocity (radians per second)
• \( \Delta \theta \) — Change in angular position (radians)
• \( \Delta t \) — Change in time (seconds)

Dimensional Formula: [T⁻¹] (Inverse of time)

3. Importance of Angular Velocity

Details: Angular velocity is crucial in physics and engineering for analyzing rotational motion, designing mechanical systems, and understanding celestial mechanics.

4. Using the Calculator

Tips: Enter the angle change in radians and time change in seconds. Both values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: Why is the dimensional formula [T⁻¹]?
A: Because angular velocity has dimensions of angle (dimensionless) divided by time (T).

Q2: How do I convert from degrees to radians?
A: Multiply degrees by π/180 (≈ 0.0174533). Our calculator requires radians.

Q3: What's the difference between angular and linear velocity?
A: Angular velocity measures rotation rate, while linear velocity measures straight-line motion.

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

Q5: What are typical units for angular velocity?
A: Radians per second (rad/s) is standard, but degrees per second and revolutions per minute are also used.