Express each angular speed in radians per second. 6 revolutions per second

Verified step by step guidance

1. Recall that one revolution corresponds to an angle of \(2\pi\) radians.
2. To convert revolutions per second to radians per second, multiply the number of revolutions per second by \(2\pi\) radians per revolution.
3. Set up the conversion: angular speed in radians per second = (6 revolutions/second) \(\times\) \(2\pi\) radians/revolution.
4. Multiply the numerical values: \(6 \times 2\pi\) to express the angular speed in terms of \(\pi\).
5. Write the final expression for angular speed in radians per second as \(12\pi\) radians per second (without calculating the decimal value).

Key Concepts

Angular Speed

Angular speed measures how fast an object rotates or revolves, typically expressed in radians per second. It quantifies the angle covered per unit time, helping to describe rotational motion precisely.

Radians and Revolutions

A radian is the standard unit of angular measure, defined as the angle subtended by an arc equal in length to the radius of the circle. One full revolution equals 2π radians, linking revolutions to radians for conversion.

Unit Conversion from Revolutions to Radians

To convert angular speed from revolutions per second to radians per second, multiply the number of revolutions by 2π. This conversion is essential for expressing angular velocity in standard SI units.