Dynamics Engineering Mechanics Gray 2nd edition problem 8.82 A rotor, spinning f

Question

Dynamics Engineering Mechanics Gray 2nd edition problem 8.82

A rotor, spinning freely about the fixed point O, consists of a thin uniform bar A B that functions as a hub and two identical blades pinned at A and B, respectively. The dimensions of the system are: d = 0.5 m, = 5 m, and w = 0.3 m. The bar A B has a mass mAB = 30 kg, and each of the blade has a mass mb = 20 kg. Each blade can be modeled as a thin uniform plate. The angular speed is wr = 100 rmp when the angle theta is equal to 90 degree. At some point, an internal mechanism causes the blades to change orientation relative to A B in such a way that theta becomes constant and equal to 180 degree. Neglecting aerodynamic forces and friction at the bearings at O, determine the angular speed of the rotor after theta = 180 degree.

Explanation / Answer

this problem can be solved by conseving the angular momentum...

L= Iw;;

first the moment of inertia can be calulated when the blades are at 90 degree.

secondly the moment of inertia can be calculated when the bladdes are at 180 degree..

equating I1w1 = I2w2;;

I1 is known w1 is known I2 is known.. w2 can b calculated..

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