Answer :
Final answer:
The question pertains to the angular momentum of a rotating wind turbine blade. The angular momentum can be determined by multiplying the blade's moment of inertia by its angular velocity. However, none of the provided options match the computed angular momentum.
Explanation:
The student's question is related to the concept of angular momentum in physics. Angular momentum (L) is defined as the rate of change of a body's angular displacement and is calculated by multiplying an object's moment of inertia (I) with its angular velocity (w).
The moment of inertia of the rotating wind turbine blade can be computed using the formula I = 0.5 * m * r^2, where m is the mass and r is the radius of the blade. Substituting the provided values into the formula yields I = 0.5 * 1430 kg * (34 m)^2 = 827,660 kg·m².
The angular velocity (w) of the blade, in radian per second, can be computed by multiplying the rotational speed in revolutions per second by 2π (as there are 2π radians in one revolution). This gives w = 0.75 rev/s * 2π rad/rev = 1.5π rad/s.
Therefore, the angular momentum (L) of the blade can be calculated using the formula L = I * w, which gives L = 827,660 kg·m² * 1.5π rad/s = 3,903,418.3 kg·m²/s. None of the provided options (A, B, C, or D) match this calculated value.
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