The height of the disk is h=15.0 cm, and the radius is, r=11.0cm. The rectangula

Question

The height of the disk is h=15.0 cm, and the radius is, r=11.0cm. The rectangular hole has a length, L=9.0cm, and width, W=8.0cm. The right side of the rectangular hole is located so that the midpoint of the right side coincides with the central axis of the disk. Determine the center of mass of a disk with a rectangular hole in it.

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Explanation / Answer

for whole disk (without hole),

center of mass, (x1, y1, z1) = (0, 0, 0)

mass = rho ( pi 11^2 x 15) = 1815pi rho

for rectangular hole,

center of mass , (x2, y2, z2) = (0, -w/2, 0 ) = (0, -4 cm , 0)

mass, m2 = - rho (L w h) = - 1080 rho

Ycm = (m1y1 + m2 y2) / (m1 + m2)

= [ (1815pi rhox 0) + (-1080rho x -4)]/ (1815pi rho - 1080 rho)

= 0.93 cm

Center of mass = (0, 0.93, 0) cm

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