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.
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
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.