Calculating the Moment of Inertia of a Helicopter Blade

What is the total moment of inertia, in kg.m², of the helicopter blades given that a typical helicopter with four blades rotates at 260 rpm and has a kinetic energy of 5.45 x 10⁵?

Moment of Inertia Calculation

Moment of Inertia is a measure of an object's resistance to changes in angular velocity. In the case of a helicopter blade, the moment of inertia can be calculated using the formula:

Moment of Inertia = (1/3) * m * r^2

Where m is the mass of each blade and r is the distance from the axis of rotation to the tip of the blade.

Given Data

Each blade has a mass of 50.0 kg and a length of 4.00 m. The distance from the axis of rotation to the tip of the blade is half of its length, which is 2.00 m.

Calculation

Substitute the given values into the formula:

Moment of Inertia = (1/3) * 50.0 kg * (2.00 m)^2

Moment of Inertia = (1/3) * 50.0 kg * 4.00 m^2

Moment of Inertia = 66.7 kg.m^2

Conclusion

The total moment of inertia of the helicopter blades is 66.7 kg.m².

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