1. What is Linear and Angular Velocity?

Linear velocity (v) is the rate of change of position along a straight path, measured in meters per second (m/s). Angular velocity (ω) is the rate of rotation about an axis, measured in radians per second (rad/s). They are related through the radius (r) of the circular path.

2. How Does the Calculator Work?

The calculator uses these fundamental equations:

Where:

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

Explanation: The linear velocity of a point rotating about an axis is equal to the angular velocity multiplied by the radius of the circular path.

3. Importance of Velocity Calculations

Details: These calculations are essential in mechanical engineering, physics, and any application involving rotational motion, such as wheels, gears, turbines, and celestial mechanics.

4. Using the Calculator

Tips: Enter any two known values (radius is always required). The calculator will compute the missing value. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between linear and angular velocity?
A: Linear velocity measures straight-line speed, while angular velocity measures rotational speed. They're related through the radius of rotation.

Q2: How do I convert RPM to rad/s?
A: Multiply RPM by 2π/60 (1 RPM = 0.10472 rad/s). You can then use this angular velocity in the calculator.

Q3: What if I know the diameter instead of radius?
A: Simply divide the diameter by 2 to get the radius before using the calculator.

Q4: Can this be used for any rotating object?
A: Yes, as long as you're considering a point at a known distance from the axis of rotation.

Q5: What are typical applications of these calculations?
A: Designing gears and pulleys, analyzing vehicle wheel motion, understanding planetary orbits, and many mechanical systems.