The momentum of the system decreases, and so does the energy. The momentum of the system remains constant, and the energy decreases. Momentum is conserved, but you cannot predict what happens to the energy. A yo-yo is swung at the end of its string in a horizontal circle. Its angular speed is constant.
Tension provides centripetal acceleration, gravity provides tangential acceleration.
A centrifuge starts from rest, and angularly accelerates to a final speed of 3000 rpm. It then continues to rotate with constant angular speed. As it spun up to speed, its tangential acceleration could have been constant. As it spun up to speed, its centripetal acceleration could have been constant. As it spun up to speed, the centripetal acceleration decreased and the tangential increased.