A medical laboratory centrifuge is modeled as a uniform solid disk of mass \(M\) and radius \(R\) (with rotational inertia \(I = \dfrac{1}{2}MR^2\)). The centrifuge initially rotates counterclockwise at a constant angular speed of \(N\) revolutions per minute. At time \(t = 0\), the motor is turned off. A constant frictional torque slows the centrifuge down, and it comes to rest after completing exactly \(n\) revolutions.