A rotating shaft supports three masses m1= 40 kg, m2 = 45 kg and m3 = 50 kg at radii 40 mm, 38 mm and 35 mm, respectivel

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A rotating shaft supports three masses m1= 40 kg, m2 = 45 kg and
m3 = 50 kg at radii 40 mm, 38 mm and 35 mm, respectively, as
illustrated in Figure 1. The supporting bearings are at A and B. At
the instant shown, (a) Calculate the relative angular direction of
reactions in bearings A and B with respect to the x-axis due to
out-of-balance masses. (b) Calculate the magnitudes of the dynamic
bearing reactions in bearings A and B due to out-of-balance masses
if the shaft is rotating at 1500 rev/min. (c) Calculate the static
reactions on bearing A. (d) Calculate the speed at which the shaft
should be run so that the total minimum total reactions in bearing
A is zero.