Question

An airplane propeller is rotating at 2000 rev/min.

Answer 1

A 1 complete revolution corresponds to an angular displacement of 2π rad, or 360º. (So there are 180º for every π rad.) Also, there are 60 seconds to 1 minute. So, the angular velocity in rad/s is

(2000 rev/min) * (2π rad/rev) * (1/60 min/s) = 200π/3 rad/s

or approximately 209.44 rad/s.

B First convert the angular velocity to degrees per second (º/s):

(200π/3 rad/s) * (180/π º/rad) = 12,000 º/s

We want to find the time t it would take for the propeller to turn 36º:

36º = (12,000 º/s) t

==>  t = 36º / (12,000 º/s) = 3/1000 s

or approximately 0.003 s.