Question

The propeller of a light plane has a length of 2.012 m and a mass of 17.36 kg. The propeller is rotating with a frequency of 3280. rpm. What is the rotational kinetic energy of the propeller? You can treat the propeller as a thin rod rotating about its center.

Answer 1

First, we need to convert the frequency into angular velocity (ω) in radians per second.

ω = (3280 rpm) * 2π/60 = 344.44 rad/s

Next, we can use the formula for rotational kinetic energy:

KE = ½ Iω²

Where I is the moment of inertia. For a thin rod rotating about its center, the moment of inertia is:

I = (1/12) M L²

Where M is the mass of the rod, and L is the length.

Plugging in the values, we get:

I = (1/12) * 17.36 kg * (2.012 m)² = 0.906 kg m²

Now we can calculate the kinetic energy:

KE = ½ * 0.906 kg m² * (344.44 rad/s)² = 52,565 J

Therefore, the rotational kinetic energy of the propeller is approximately 52,565 J.