Question

1 revolution is equivalent to:
A) $\pi $ Radians
B) $2\pi $ Radians
C) $3\pi $ Radians
D) $4\pi $ Radians

Answer 1

Hint: A full revolution is the total turn, which completely rotates ${360^\circ }$. When a body revolves around a point with some angular velocity and reaches its starting point after a total turn of ${360^\circ }$ then it is called one revolution.
All spherical things rotate ${360^\circ }$ in their full revolution.

Complete step by step answer:
When a body rotates as the angle formed between initial and final position is ${360^\circ }$ then the body completes its one full revolution.
Revolution means the turning of a point along the circumference of a spherical body.
The circumference of any circular body/spherical body is equal to the $2\pi $ times of the radius.
So, circumference of the circle $ = 2\pi \times radius$
Or we can write circumference of the circle $ = 2\pi r$
Now, we are going to find an angle formed in one complete revolution.
According to the definition of revolution, the total turn of anybody along its circumference is equal to the circumference of the body i.e. known as the angular displacement of the body.
If $r$ be the radius of the circular body/path of motion of the body. So, angle forms in completing a full revolution will be found as we know that
$Angle = \dfrac{{Arc}}{{radius}}$
Here, arc is the total angular displacement in one revolution.
$Angle = \dfrac{{circumference}}{{radius}}$
Because in the case of one complete revolution, the arc is the total circumference of the circular path.
Substituting the values of circumference and radius-
$Angle = \dfrac{{2\pi r}}{r}$
$ \Rightarrow Angle = 2\pi $ Radians
Hence, in one complete revolution, we get $2\pi $ radians.

Therefore, option B is correct.

Additional information:
If we want to change radians to degrees then $\pi = {180^\circ }$
So,
$
  2 \pi = 2 \times {180^\circ } \\
 \Rightarrow 2 \pi = {360^\circ } \\
$
Which shows an angle of ${360^\circ }$ (complete angle). Hence, in a complete revolution the displacement of the body along its circumference is zero.

Note:
The one revolution describes the angle form of ${360^\circ }$s the increase of revolution will be the multiple of $2 \pi $ and can be written as $2n \pi $ where $n$ is the natural number showing the number of revolutions.
Revolutions per minute and revolutions per second are the main units of describing frequency of a moving particle in circular/rotational motions.