Why is the RPM achieved on a reciprocating machine in general lesser than that obtained in a rotating machine? For example, an IC engine typically provides an RPM of about 2500 while a turbine can go as high as 80,000 RPM. The inertia and the repetitive change in direction of motion in case of reciprocating machine is one aspect, but is there an analytical justification/limitation on the RPM?
A turbine has its mass more widely distributed, so that the forces needed to accelerate each part are spread over larger area cylindrical shells and not transmitted through a narrow connecting rod, so the stresses in the blades of a turbine are much less than the stresses in the push rod of a reciprocating engine working at the same angular speed.
To understand this statement more deeply, think of the mass of a piston divided up amongst many equal spokes and what the stresses in these spokes as opposed to the stresses in a single push rod shoving the same mass, but concentrated, to and fro.
It is also likely that one can balance (i.e. achieve zero oscillating force on the bearings through even mass distribution) a nearly axisymmetric object like a turbine than one far from axisymmetry much more accurately for the same mechanical tolerances on the parts.
A factor which I do not understand but which may also be important here is the rate of reaction for the fuel burning happening inside the engine, so a chemist or thermodynamicist can answer this part of the question. The reactants probably have a much longer time to burn more evenly as they flow through a turbine than in the cylinder of a reciprocating engine working at the same angular frequency. This rate will limit the speed as well.