The cat righting reflex is a cat's innate ability to orient itself as it falls in order to land on its feet. The righting reflex begins to appear at 3–4 weeks of age, and is perfected at 7 weeks. The minimum height required for this to occur in most cats would be around 30 cm. You are part of an engineering team trying to reproduce this in a mechanical cat. Your prototype, aptly named Katt, when dropped motionless, upside down from 2.5 m, can right itself before it hits the ground by rotating its "tail". Katt’s body is a solid cylinder 30 cm in length and 15 cm in diameter, with a mass of 3.0 kg. Attached to the center of one end of the body is Katt's tail, a 20-cm long rod which extends out perpendicular to Katt's body and has only 10% the mass of the body. The tail will rotate due to a small electric motor in the body that produces a constant torque. In order to order the piece, determine the angular speeds it will need to deal with.