# Linear Velocity to Angular Velocity Calculator

## About Linear Velocity to Angular Velocity Calculator (Formula)

A Linear Velocity to Angular Velocity Calculator is a tool used to convert linear velocity (the rate of change of position in a straight line) into angular velocity (the rate of change of angular displacement). This calculator is essential in physics, engineering, and mechanics, particularly when translating between linear and rotational motion.

The formula for converting linear velocity to angular velocity involves the radius of rotation:

Angular Velocity (ω) = Linear Velocity (v) / Radius (r)

Where:

• Angular Velocity (ω) is the rate of change of angular displacement, measured in radians per second (rad/s).
• Linear Velocity (v) is the rate of change of position in a straight line, often measured in meters per second (m/s).
• Radius (r) is the distance from the center of rotation to the point at which linear velocity is measured, typically measured in meters (m).

To use the Linear Velocity to Angular Velocity Calculator formula, follow these steps:

1. Measure the linear velocity of the object in meters per second.
2. Determine the radius of rotation, which is the distance from the center of rotation to the point where linear velocity is measured.
3. Plug the values of linear velocity and radius into the formula: Angular Velocity (ω) = Linear Velocity (v) / Radius (r).
4. Calculate the angular velocity. The result indicates the rate of change of angular displacement in radians per second.

This conversion is fundamental for understanding rotational motion, especially when dealing with scenarios like wheels, gears, and other rotating objects. It helps bridge the gap between linear and angular measurements and is crucial for various mechanical and engineering applications.

Keep in mind that angular velocity is a vector quantity and has both magnitude and direction, while linear velocity is scalar.