Question

The blades of a fan are rotating at 392 rev/min. What is the speed of rotation in radians per second?

1) 6.5 rad/s
2) 12.3 rad/s
3) 20.6 rad/s
4) 25.9 rad/s

Answer 1

The fan blades rotating at 392 rev/min have an angular velocity of approximately 41.0 rad/s, after converting from rev/min to rev/s and then to rad/s.

Step-by-step explanation:

To determine the speed of rotation in radians per second for a fan spinning at 392 rev/min, we can start by converting revolutions per minute to revolutions per second, and then convert revolutions into radians. There are 2π radians in one revolution. The steps are as follows:

1. Convert revolutions per minute (rev/min) to revolutions per second (rev/s) by dividing by 60, since there are 60 seconds in one minute:
2. 392 rev/min ÷ 60 = 6.5333... rev/s
3. Convert revolutions per second to radians per second (rad/s) by multiplying by 2π:
4. 6.5333... rev/s × 2π rad/rev = 41.0 rad/s

Thus, the blades of a fan rotating at 392 rev/min are spinning at an angular velocity of approximately 41.0 rad/s.