Aplayground carousel is rotating counterclockwise about its center on frictionless bearings. a person standing still on the ground grabs onto one of the bars on the carousel very close to its outer edge and climbs aboard. thus, this person begins with an angular speed of zero and ends up with a nonzero angular speed, which means that he underwent a counterclockwise angular acceleration. the carousel has a radius of 1.61 m, an initial angular speed of 3.18 rad/s, and a moment of inertia of 124 kg·m2. the mass of the person is 47.7 kg. find the final angular speed of the carousel after the person climbs aboard.

Air enters a gas turbine with two stages of compression and two stages of expansion at 100 kpa and 17°c. this system uses a regenerator as well as reheating and intercooling – the intercooler returns the air to the inlet temperature. the pressure ratio across each compressor is 4 ; 300 kj/kg of heat are added to the air in each combustion chamber; and the regenerator operates perfectly while increasing the temperature of the cold air by 20°c. determine the system’s thermal efficiency. assume isentropic operations for all compressor and the turbine stages and use constant specific heats at room temperature. (0.378)