1. What is Angular Speed?

Definition: Angular speed is the rate at which an object rotates or revolves relative to another point, measured in radians per second (rad/s).

Purpose: It describes how fast the angular position of an object changes with time.

2. Angular Speed Formula

The calculator uses the formula:

Where:

• \( \omega \) — Angular speed (rad/s)
• \( \Delta \theta \) — Change in angle (radians)
• \( \Delta t \) — Change in time (seconds)

3. Dimensional Formula

The dimensional formula for angular speed is:

Explanation: Since angle is dimensionless (radians are a ratio), the dimensions come only from the time component in the denominator.

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 angle is dimensionless (no [M], [L], or [T] components), leaving only the time component in the denominator.

Q2: What's the difference between angular speed and angular velocity?
A: Angular speed is a scalar (magnitude only), while angular velocity is a vector (magnitude and direction).

Q3: How do I convert from degrees to radians?
A: Multiply degrees by π/180 (≈ 0.01745).

Q4: What are typical angular speed values?
A: Earth's rotation ≈ 7.27×10⁻⁵ rad/s, CD player ≈ 200-500 rad/s.

Q5: Can angular speed be negative?
A: In this calculator no, but physically it indicates direction of rotation.