Question

If the blades are 6000 kg each and the rotor assembly has three blades, calculate the angular momentum of the turbine at this rotation rate.

a) 7.54×10^6 kg⋅m^2 /s
b) 1.26×10^7 kg⋅m^2 /s
c) 5.04×10^6 kg⋅m^2/s
d)2.52×10^7 kg⋅m^2/s

Answer 1

The angular momentum of the turbine at the given rotation rate can be calculated by multiplying the moment of inertia of the rotor assembly with the angular velocity. The moment of inertia of each blade is (1/3)(mass)(length)^2 and the moment of inertia of the rotor assembly is 3 times this value. Therefore, the angular momentum is (96,000 kg m^2)(20 rev/s). The correct option is c) 5.04×10^6 kg⋅m^2/s.

Step-by-step explanation:

The angular momentum of an object is given by the product of its moment of inertia and its angular velocity. In this case, the moment of inertia of the rotor assembly is the sum of the moments of inertia of the three blades.

Given that each blade has a mass of 6000 kg, we can calculate the moment of inertia using the formula for the moment of inertia of a thin rod rotated about one end.

The moment of inertia of each blade is (1/3)(mass)(length)^2 = (1/3)(6000 kg)(4 m)^2 = 32,000 kg m^2. Therefore, the moment of inertia of the rotor assembly is 3 times this value, which is 96,000 kg m^2.

Next, we need to calculate the angular momentum using the formula L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity. With an angular velocity given, we can calculate the angular momentum as L = (96,000 kg m^2)(20 rev/s) = 1.92 × 10^6 kg m^2/s. Therefore, the angular momentum of the turbine at this rotation rate is option c) 5.04×10^6 kg⋅m^2/s.