A three-phase, \(60-\mathrm{Hz}, 500-\mathrm{MVA}, 11.8-\mathrm{kV}\), 4-pole steam turbine-generating unit has an \(\mathrm{H}\) constant of 5 p.u.-s. Determine:

(a) \(\omega_{\text {syn }}\) and \(\omega_{m \text { syn }}\);

(b) the kinetic energy in joules stored in the rotating masses at synchronous speed;

(c) the mechanical angular acceleration \(\alpha_{m}\) and electrical angular acceleration \(\alpha\) if the unit is operating at synchronous speed with an accelerating power of \(500 \mathrm{MW}\).