An ice skater is in a spin, she pulls her arms in and she spins faster, she lets her arms extend outward and then she starts to slow down. She will probably weigh on a weigh scale about the same weight during this spin cycle.
Now let us connect an electric motor to her to make her spin faster as she extends her arms outward. Would angular momentum still be conserved? It seems to me that it would not.
Also would she still have the same weight? I think she will weigh less as she is being accelerated by the electric motor.