Question

What's the difference between revolutions and radians?

Answer 1

The length of the full circle divided by the radius, or $\dfrac{{2r}}{r}$ , or $2\pi$ is the magnitude in radians of one complete revolution $\left( {{{360}^ \circ }} \right)$ . As a result, two radians equal ${360^ \circ }$ , and one radian equals $\dfrac{{180}}{{57.295779513082320876}}$ degree.

Complete step by step answer:
Let u first know the definition of both after that we will get to their difference.
Radian: The radian is a SI unit that can be used to measure angles. Furthermore, it is the standard unit of angular measurement used in a variety of fields of mathematics. The length of an arc on a unit circle is numerically equivalent to the measurement in radians of the angle it subtends.

Revolution: The term "revolution" is frequently used interchangeably with "rotation." However, revolution is referred to as an orbital revolution in many domains, such as astronomy and related subjects. It refers to the movement of one body around another.

Now, let us understand their difference: A factor of $2\pi$ . One revolution traces out $2\pi$ ​radians.
Explanation: the angle subtended by an arc of length equal to the radius is called a radian. In other words, if the radius is r, the arc length equals r. The length of an arc must be $2\pi r$ in order for it to cover a full revolution, hence the angle is $2\pi$radians.

Note: Angles are universally measured in radians in calculus and most other fields of mathematics beyond practical geometry. This is due to the mathematical "naturalness" of radians, which allows for more elegant presentation of a number of fundamental results.