Generator manufacturers often use the term \(\mathrm{WR}^{2}\), which is the weight in pounds of all the rotating parts of a generating unit (including the prime mover) multiplied by the square of the radius of gyration in feet. \(\mathrm{WR}^{2} / 32.2 \) is then the total moment of inertia of the rotating parts in slug- \(\mathrm{fl}^{2}\).

(a) Determine a formula for the stored kinetic energy in ft-lb of a generating unit in terms of \(\mathrm{WR}^{2}\) and rotor angular velocity \(\omega_{m}\)

(b) Show that \(\mathrm{H}=\frac{2.31 \times 10^{-4} \mathrm{WR}^{2}(\mathrm{rpm})^{2}}{\mathrm{~S}_{\text {rated }}}\) per unit-seconds where \(S_{\text {rated }}\) is the voltampere rating of the generator, and rpm is the synchronous speed in \(\mathrm{r} / \mathrm{min}\). Note that \(1 \mathrm{ft}-\mathrm{lb}=746 / 550=1.356\) joules,

(c) Evaluate \(\mathrm{H}\) for a three-phase generating unit rated 750 MVA, \(3600 \mathrm{r} / \mathrm{min}\), with \(\mathrm{WR}^{2}=4,000,000 \mathrm{lb}-\mathrm{ft}^{2}\).