Try this problem, useful for Physics Olympiad, based on the propeller’s angular velocity.

The Problem:

An airplane propeller is rotating at (1900)rpm (rev/min).

(a)Compute the propeller’s angular velocity in rad/s.

(b) How many seconds does it take for the propeller to run through (35^\circ)?

Solution:

An airplane propeller is rotating at (1900)rpm (rev/min).

(1)rpm = (2\pi /60)$$ \omega=(1900)(2\pi /60)=199 $$Hence, the propeller’s angular velocity (\omega)=(199)rad/s.

b) (35^\circ)(\pi/180^\circ)=(0.611)rad.

Since angular velocity (\omega)=199rad/s, the time required for the propeller to run through (35^\circ)=$$ \frac{0.611}{199}=3.1\times10^{-3}s$$