A fairground target consists of a uniform circular disk of mass M and radius a that can turn freely about a diameter which is fixed in a vertical position. Initially the target is at rest.
A bullet of mass m is moving with speed u along a horizontal straight line at right angles to the target. The bullet embeds itself in the target at a point distance b from the rotation axis.
Find the final angular speed of the target. [The moment of inertia of the disk about its rotation axis is Ma2/4.] Show also that the energy lost in the impact is
1/2mu2 (Ma2 / (Ma2+4mb2))