The manufacturer of a propeller for a small aircraft mandates a maximum operating angular velocity of 300 rad/s. Determine whether it is safe to install this propeller on an aircraft whose engine is expected to run at a maximum of 2800 rpm.
To determine whether it is safe to install the propeller on the aircraft, we need to compare the maximum angular velocity specified by the manufacturer of the propeller with the maximum angular velocity the engine is expected to run at.
First, we need to convert the engine’s maximum rotational speed from rpm to radians per second:
1 revolution = 2π radians
Therefore,
2800 rpm = (2800 revolutions/1 minute) × (2π radians/1 revolution) × (1 minute/60 seconds)
Simplifying the units,
2800 rpm = (2800 × 2π)/60 radians per second
2800 rpm ≈ 293.33 radians per second
Now we have the engine’s maximum angular velocity as approximately 293.33 rad/s.
To determine if it is safe to install the propeller, we compare this value with the manufacturer’s specified maximum operating angular velocity of 300 rad/s.
Comparing the values, we see that the engine’s maximum angular velocity (293.33 rad/s) is less than the manufacturer’s specified maximum operating angular velocity (300 rad/s). Therefore, it is safe to install this propeller on the aircraft.