A disk-shaped merry-go-round of radius 3.03 mand mass 145 kg rotates freely with an angular speed of 0.681 rev/s . A 65.4 kg person running tangential to the rim of the merry-go-round at 3.41 m/s jumps onto its rim and holds on. Before jumping on the merry-go-round, the person was moving in the same direction as the merry-go-round's rim. What is the final angular speed of the merry-go-round?

Oxygen gas enters well-insulated diffuser at 25 lbf/in.2, 420r, with a velocity of 860 ft/s through a flow area of 1.6 in.^2. at the exit, the flow area is 12 times the inlet area, and the velocity is 19 ft/s. the potential energy change from inlet to exit is negligible. assuming ideal gas behavior for the oxygen and steady-state operation of the diffuser, determine the following: (a) the exit temperature, in r(b) the exit pressure, in lbf/in.^2 (c) the mass flow rate, in lb/s