A circus acrobat while performing spins brings his limbs closer to the body. Due to this Angular Momentum is conserved but K.E. is not conserved. Because when the moment of inertia decreases, rotational kinetic energy increases as work is done in decreasing the moment of inertia of the body.
Conservation of Angular Momentum
Angular momentum of a system is conserved as long as there is no net external torque acting on the system, the earth has been rotating on its axis from the time the solar system was formed due to the law of conservation of angular momentum,