Final answer:
The moment of inertia of a semicircular lamina of mass m and radius r about an axis through its center of mass and perpendicular to its plane is (1/4)mr^2.
Step-by-step explanation:
The moment of inertia of a semicircular lamina of mass m and radius r about an axis through its center of mass and perpendicular to its plane can be calculated using the formula for the moment of inertia of a disk.
The moment of inertia of a disk about an axis through its center is given by I = (1/2)mR^2, where m is the mass of the disk and R is the radius.
In this case, the disk is a semicircle, so we need to multiply the moment of inertia of the disk by a factor of 1/2 to account for the fact that only half of the disk is present.
Therefore, the moment of inertia of the semicircular lamina is given by I = (1/2)(1/2)mr^2 = (1/4)mr^2.