A uniform disk of radius R is cut in half so that the remaining half has mass M

Question

A uniform disk of radius R is cut in half so that the remaining half has mass M (the figure (Figure 1) a). What is the moment of inertia of this half about an axis perpendicular to its plane through point A? Express your answer in terms of the given quantities. Why did your answer in part A come out the same as if this were a complete disk of mass M Express your answer in terms of the given quantities. What would be the moment of inertia of a quarter disk of mass M and radius R about an axis perpendicular to its plane passing through point B (the figure (Figure 1) b)?

Explanation / Answer

moment of inertia of a disk of complete disk I = (1/2)*(2*M)*R^2

A) moment of inertia of a semicircular disk I1 = I/2 = (1/2)*M*R^2

B)

moment of inertia of a disk of complete disk I = (1/2)*(4*M)*R^2

moment of inertia of quarter part of disk I2 = I/4= (1/2)*(M)*R^2

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