A first, simple theory of thermal fluctuations of ideal rigid rotors is presented, along with some representative measurements and analysis of a real rotor. The ideal rotor has a power spectrum of fractional frequency fluctuations with two regions. At low frequency it is flat, and at high frequency it varies as ω^-2. A related measure, the level of fluctuations as a function of measuring time (the Allan variance), is presented. Our present magnetically suspended rotors are shown to have an excess noise amplitude of about 10⁴ times the ideal level. "Electronic cooling" by feedback can provide great improvement in both the noise amplitude and spectral behavior of the ideal rotor.