The angular velocity of a fan blade is 4.6 radians per second. Approximately how many revolutions does the fan blade make in 2.4 minutes?

Answer 1

The trick to this question is that we need to make sure the units are compatible.

Let's first convert 2.4 minutes into seconds: there is 60 seconds in a minute, so 2.4 minutes = 60*2.4 = 144 seconds.

This means in 2.4 minutes, the fan would have rotated 4.6 [rad/s] * 144s = 662.4 radians

But 1 radian = 0.159155 revolutions, so the fan has rotated 0.159155 * 662.4 = 105.42 revolutions