Question

The angular speed of a fly wheel making $120$ revolutions per minute is
A.$\pi $ rad/sec.
B.$2\pi $ rad/sec.
C.$4\pi $ rad/sec.
D.$4{\pi ^2}$ rad/sec.

Answer 1

Hint: The angular speed of a wheel is directly proportional to the frequency or the numbers of revolutions per minute/second.
Formula Used: Angular speed $\omega {\text{ = 2}} \times \pi \times \eta $ rad/sec.
Where $\eta $ is the frequency of the wheel.

Complete step-by-step answer:
Fly wheel makes$120$ revolutions per minute which is the frequency of the wheel ($\eta $).
So revolutions made by wheel per second ($\eta $)= $\dfrac{{120}}{{60}}$ =$2$
Now, the angular speed of the wheel is radian per second.
 $\omega {\text{ = 2}} \times \pi \times \eta $
$\omega {\text{ = 2}} \times \pi \times 2$
$\omega {\text{ = 4}}\pi $
The angular speed of the wheel is $4\pi $ rad/sec.

Note: In circular or rotational motion, the time rate with which angular displacement took place of an object is known as the angular speed.