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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.

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