Assume a disk of uniform mass density ? and radius R. A circular hole of radius

Question

Assume a disk of uniform mass density ? and radius R. A circular hole of radius a is cut off the disk at distance b from the center as shown in the figure. (a) Where is the center of gravity of the new shape? (b) What is the moment of Inertia of the new shape about an axis perpen- dicular to it?s plane through the center of the uncut cylinder, P? (c) Substitute in answers in (a) and (b) for R = 10.0 cm, a = 2.00 cm and b = 7.00 cm.

(Please give a detailed answer, and as fast as possible. Will rate lifesaver, thank you!)

Explanation / Answer

a) center of gravity will change for x axis only and will remain same for y axis
so shift in center of gravity along x axis = (x102x0 - x22x 7) / (x102 -  x22) = 0.75 cm

b) Ixx = (/4 )x104 - (/4 )x24 = 7841.4 cm4

Iyy =  (/4 )x104 - (x22 x 72 ) = 7238.23 cm4

so Izz = 7841.4 + 7238.23 = 15079.63 cm4

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