Hmm, can this explanation work in reverse? I've always found the conservation of momentum to be very confusing. Why does a spinning body cause an orthogonal rot

Hmm, can this explanation work in reverse? I've always found the conservation of momentum to be very confusing. Why does a spinning body cause an orthogonal rotation upon itself and thus any rigid body it's attached to? I know there's math to explain it, but it just doesn't seem intuitive to understand.