The planetary gear set of an automatic transmission consists of three planet gears A, B,...

The planetary gear set of an automatic transmission consists of three planet gears A, B, and C, mounted on carrier D, and meshed with the sun gear E and ring gear F. By controlling which gear of the planetary set rotates and which gear receives the engine's power, the automatic transmission can alter a car's speed and direction. If the carrier is rotating with a counterclockwise angular velocity of while the ring gear is rotating with a clockwise angular velocity of determine the angular velocity of the planet gears and the sun gear. The radii of the planet gears and the sun gear are 45 mm and 75 mm, respectively.