You have a 3 ft long cylinder with a radius of 025 ft A hole

You have a 3 ft long cylinder with a radius of 0.25 ft. A hole is cut through center of the cylinder (all the way through) with a radius of 0.05 ft. what is the I_2z for the combined shape? Two plates are attached to each with two different masses, what is the center of gravity in the X_1 Y_1 + Z directions

Solution

Case 1:

M.O I of cylinder = mr^2/2 = m*0.25*0.25/2 = 0.03125m
M.O.I of removed cylinder = m\'(0.05)^2/2 = 0.00125m\'
now, m\' = m*(0.05/0.25)^2 = 0.04m
M.O.I of removed cylinder = 0.00005m
Net M.O.I = 0.0312m [where m is mass of cylinder]

Case 2:

C.O.G
x-coordinate = 2.5ft
y-coordinate = 1ft
z - cordinate = z (from bottom of the bottom plate)
Now, m2*0.25 + m1*0.75 = (m1+m2)*z
30*0.25 + 75*0.75 = 110*z
z = 0.58 inch in the z direction