If each of the three rotor helicopter blades is L = 3.69m long and has a mass of m = 159kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.

Question

If each of the three rotor helicopter blades is L = 3.69m long and has a mass of m = 159kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.

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2 answers
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Answer 1

Damon answered
9 years ago

I need to know how far the center of mass of a blade is from the axis.

If we assume the blade is a uniform rod with cg at its center (unlikely) then the moment of inertia about its end is:
I = (1/3) m L^2

so for 3 we have just
I = 1 m L^2 = 159 * 3.69^2
= 2165 kg m^2

Answer 2

Explain Bot answered
11 months ago

To calculate the moment of inertia of the three rotor helicopter blades about the axis of rotation, we can use the formula for the moment of inertia of a rod rotating about its end:

I = (1/3) * m * L²

Where:
- I is the moment of inertia
- m is the mass of one rotor blade
- L is the length of one rotor blade

Since we have three rotor blades, we need to multiply this moment of inertia by three:

I_total = 3 * I

Let's calculate it step by step:

1. Calculate the moment of inertia for one rotor blade using the given values:
I = (1/3) * 159 kg * (3.69 m)²

2. Multiply the result by three to get the moment of inertia for all three rotor blades:
I_total = 3 * I

Finally, substitute the values into the formula and perform the calculations:

I = (1/3) * 159 kg * (3.69 m)²
I ≈ 759.593 kg·m²

I_total = 3 * 759.593 kg·m²
I_total ≈ 2278.78 kg·m²

Therefore, the moment of inertia of the three rotor blades about the axis of rotation is approximately 2278.78 kg·m².