Beer & Johnston — Torsion: Problem 3.82

3.82 A 1.5-m-long tubular steel shaft (\(G = 77.2 \text{ GPa}\)) of 38-mm outer diameter \(d_1\) and 30-mm inner diameter \(d_2\) is to transmit 100 kW between a turbine and a generator. Knowing that the allowable shearing stress is 60 MPa and that the angle of twist must not exceed 3°, determine the minimum frequency at which the shaft can rotate.