By evaluating the "volume" of the relevant region of its phase space, show that the number of microstates available to a rigid rotator with angular momentum \(\leq M\) is \((M / \hbar)^{2}\). Hence determine the number of microstates that may be associated with the quantized angular momentum \(M_{j}=\sqrt{ }\{j(j+1)\} \hbar\), where \(j=0,1,2, \ldots\) or \(\frac{1}{2}, \frac{3}{2}, \frac{5}{2}, \ldots\) Interpret the result physically.