Question

The angular velocity in rad/s of the flywheel making $300{\text{ rpm}}$:
A. $600\pi $
B. $20\pi $
C. $10\pi $
D. $30$

Answer 1

Hint:The angular velocity of the object is the rate of change of the angular displacement with respect to time. The angular displacement is the displacement of the object moving in the circular path. The unit of the angular velocity is radian per second, in the SI system.

Complete step-by-step solution:
According to the question it is given that the angular velocity in rad/s of the flywheel making $300{\text{ rpm}}$.
The angular velocity is described as the number of revolutions per unit time and it can be denoted in radian per second or revolution per minute.
There are seven fundamental units: length, mass, time, current, temperature, luminous intensity and the amount of substance. The units are meter, kilogram, second, ampere, kelvin, candela and mole.
The SI unit of the angular velocity is radian per second.
The value of the angular velocity in radian per minute is 300.
Write the formula for conversion of angular velocity in radian per second as shown below.
$ \Rightarrow \omega = \dfrac{{2\pi N}}{{60}}$ (1)
Where, $N$ is the angular velocity in radian per minute and $\omega $ is the angular velocity in radian per second.
Substitute $300$ for $N$ in the equation (1), we get
$
   \Rightarrow \omega = \dfrac{{2\pi \left( {300} \right)}}{{60}} \\
   \Rightarrow \omega = 10\pi \\
 $
From the above calculation it is concluded that the angular velocity in rad/s of the flywheel making $300{\text{ rpm}}$ is $10\pi $.
Hence, the option C is correct.

Note:- The radian per minute is the radian observed in one minute. The radian per second is the radian observed in one second. Thus, radian per minute is converted into radian per second by dividing by 60.