A rotor consists of four horizontal blades each of length L = 3.9 in and mass m

Question

A rotor consists of four horizontal blades each of length L = 3.9 in and mass m = 89 kg cantilevered off of a vertical shaft. Assume that each blade can be modeled as having its mass concentrated at its midpoint. The rotor is initially at rest when it is subjected to a moment M = beta t, with beta = 62 N m/s. Determine the angular speed of the rotor after 9 s. The angular speed is rad/s The moment is aligned with the shaft (vertical direction). The velocity of the center of each blade is circumferential (r ) and the distance from the shaft to the blade center is radial, so the angular momentum of each blade is also in the vertical direction. Even though the angular impulse equation is inherently a vector expression, both moment and angular momentum are aligned with the vertical direction in this problem so the angular impulse equation can be written as a scalar equation in the vertical direction.

Explanation / Answer

Been a little while, but I think I got it down. :) So a little housekeeping: model the blades as a single massless rod with a weight a the end. So we have radius 1.95 and mass of 356. We start off with the kinetic energy equation for a linear body and transform it for rotation: KE=1/2*m*v^2 Note:velocity = radius * angular velocity (v = r * w) KE = 1/2*m*(r*w)^2 With the simplified model of the rotor, we can plug in the radius and mass to get: KE=1/2*356*1.95^2*w^2 We just need to find KE, and divide KE by everything on the rightside but omega (w). Power = (Work or Energy)/time = Force * distance / time = N * m / s

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