1. Flat disk of radius R has circular hole of radius R/2 that is positioned as s

Question

1.      Flat disk of radius R has circular hole of radius R/2 that is positioned as shown on the picture. Mass of the disk is m. Find moment of inertia I of such disk with respect to the axis going through the geometrical center of the disk O perpendicular to the disk%u2019s plane.

http://snag.gy/mpqcb.jpg

The The diagram is above, listed as Problem 1.

Flat disk of radius R has circular hole of radius R/2 that is positioned as shown on the picture. Mass of the disk is m. Find moment of inertia I of such disk with respect to the axis going through the geometrical center of the disk O perpendicular to the disk%u2019s plane.

Explanation / Answer

Moment of Intertial of the Disk Disslocated from the Figure About the Center of the FUll Circular by Using Parallel axis theorem = 0.5*(m/4)*(R/2)^2 + (m/4)*(R/2)^2

= (3/2)*(m/4)*(R/2)^2

= (3/32)mR^2

So required Moment of Inertia = mR^2 - (3/32)mR^2

= (29/32)mR^2

= 0.90625mR^2

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