Question

If $n$ is the frequency of rotation of a body, its angular velocity is ____.
A. 2πn
B. 4πn
C. 6πn
D. πn

Answer 1

To understand the relationship between angular velocity and frequency, we need to dig deeper into the definition of angular velocity. Also establishing a mathematical relation is the main goal.

Complete answer:
At a given time period, the number of rotations made by a rotating object around a centre is the angular velocity of that object. Whereas frequency is the number of revolutions that an object makes per some given unit of time.

Therefore, if an object makes one full revolution, then its frequency will be measured in terms of $\dfrac{rev}{\sec }$. And the angular velocity is the number of radians per some given unit of time, that is, $\dfrac{rad}{\sec }$.Now, the relation between revolution and radians is that one revolution is $2\pi$ radians per second.

Therefore, the relation of frequency in terms of radians becomes $2\pi$ per the second square, but angular velocity in terms of radians is radians per second and so the frequency becomes angular velocity by $2\pi$. So, if angular velocity is $w$ and frequency is $n$ (as per the question), the relation becomes $n=\dfrac{w}{2\pi }$ , that is the angular velocity will be $w=2\pi n$.

Hence, the correct answer is option A.

Note: Both angular velocity and frequency can be expressed in terms of time period too. This way we can relate both angular velocity and frequency with their mathematical terms and generate two different equations with the me period of a rotating object.