The Pegasus in the P1127 and later the Harrier was, and is, the result of true genius.
Just simply contra-rotating the low pressure and high pressure compressor spools (each with attached turbines) is not enough. It's the product of each assembly's moment of inertia with its angular rotation speed, its angular momentum, that has to be equal and opposite to the other - so that the net angular momentum of the engine is zero.
Because the two spools rotate at different speeds, they had to be designed so that their moments of inertia came out at the right values for this to be the case in the hover. Moreover, this principle had to be maintained throughout the engine's development and thrust growth.
A design triumph, thanks to Sir Stanley Hooker and team.