Why do the Pegasus turbine rotors spin in opposite directions?

In the Rolls-Royce Pegasus, the low-pressure and high-pressure shafts rotate in opposite directions, an unusual solution that markedly reduces the gyroscopic effects that would otherwise cause control problems for the aircraft at low speed. The engine not only drives the aircraft forward but also directs the thrust, both from the fan and from the turbine, downwards through swivelling nozzles. That thrust is divided among four rotating nozzles. The idea of four vectored-thrust nozzles, with the hot gases through the two rear ones, was proposed by the designer Ralph Hooper, building on a suggestion from Lewis.

In May 1957 the team received a letter of support from Sydney Camm of Hawker Aviation, stating that they were looking for a replacement for the Hawker Hunter. Development of the P.1127 design formally began that same year under Sir Sydney Camm, Ralph Hooper of Hawker Aircraft, and Stanley Hooker of the Bristol Engine Company. Instead of rotors or direct thrust, the P.1127 used an innovative vectored-thrust turbofan, the Pegasus. Development of the engine then advanced in parallel with that of the aircraft. Project engineer Gordon Lewis considered the close cooperation between Hawker, the airframe company, and Bristol, the engine company, to be one of the key factors that allowed Harrier development to continue despite technical obstacles and political setbacks.

The P.1127 first flew, in tethered hover, on 21 October 1960, powered by the BE53/3 (Pegasus 2). The P.1127 achieved free hover on 19 November that same year and made the transition to wing-borne flight in 1961. The engine is mounted in the centre of the Harrier, so to change it the wing had to be removed after propping the fuselage up on trestles.