1. What is Angular and Linear Speed?

Angular speed (ω) measures how fast an object rotates or revolves relative to another point, expressed in radians per second (rad/s). Linear speed (V) measures the actual distance traveled per unit time, expressed in meters per second (m/s).

2. How Does the Calculator Work?

The calculator uses the linear speed formula:

Where:

• \( V \) — Linear speed (m/s)
• \( \omega \) — Angular speed (rad/s)
• \( r \) — Radius (m)

Explanation: The formula converts rotational motion to linear motion by multiplying angular speed by the radius of rotation.

3. Importance of Speed Calculation

Details: Calculating linear speed from angular speed is essential in mechanical engineering, physics, and various applications involving rotating systems like wheels, gears, and turbines.

4. Using the Calculator

Tips: Enter angular speed in rad/s and radius in meters. Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between angular and linear speed?
A: Angular speed measures rotation rate (angle per time), while linear speed measures straight-line distance traveled per time.

Q2: How do I convert RPM to rad/s?
A: Multiply RPM by 2π/60 (since 1 revolution = 2π radians and 1 minute = 60 seconds).

Q3: Does this formula work for any circular motion?
A: Yes, the formula V = ω × r applies to any object moving in a circular path with constant angular speed.

Q4: What if the angular speed is not constant?
A: This calculator assumes constant angular speed. For variable angular speed, instantaneous linear speed would require calculus methods.

Q5: Can I use different units with this calculator?
A: The calculator is designed for rad/s and meters. Convert other units to these standard SI units before calculation.