Atypical helicopter has four blades that rotate at 334 rpm and have a total kinetic energy of 4.55 105 j. what is the magnitude of the total angular momentum of the blades about the axis of rotation?

the magnitude of the total angular momentum of the blades is 743.71 kg·m²

Explanation:

Converting the angular speed into radians per second:

ω = 334 rpm · (2π rad / 1 rev) · (1 min / 60 s)

ω = 34.98 rad/s

The rotational kinetic energy of the blades is given by:

EK = 1/2 I ω²

where

Therefore, rearranging the above equation, we get:

1/2 I ω² = EK

I ω² = 2 EK

I = 2(EK) / ω²

I = 2(4.55 × 10⁵ J) / (34.98 rad/s)²

I = 743.71 kg·m²

Therefore, the magnitude of the total angular momentum of the blades is 743.71 kg·m².