The unsteady flow of a homogeneous viscous fluid past a straight circular cylinder (radiusl*)confined between two infinite parallel plates (a distanced*apart) relative to a rapidly rotating frame is considered. The cylinder is impulsively started from rest to a uniform velocity. The unsteady form of the boundary-layer equations for a rotating fluid is used to examine the flow Rossby numberRo∼O(E1/2),whereE≪1is the Ekman number. A range of values of the non-dimensional parameterN=lE1/2/Ro(wherel=l*/d*)is considered. For0⩽N<1,the flow pattern resembles that of the non-rotating case(N=0).Initially, the wall shear around the cylinder is positive everywhere. After a time, flow reversal begins at the rear stagnation point and then the position of zero wall shear moves upstream, towards the front stagnation point. The boundary-layer thickness in the region of reversed flow grows with time until a singularity/eruption at a point in the flow occurs. The boundary-layer equations are written in terms of Lagrangian coordinates in order to numerically investigate the finite-time singularity for0⩽N<1.The flow close to the rear stagnation point is also examined in detail for a range of values ofNand results are compared with the large-time asymptotic forms for the growth of the displacement thickness. The analysis suggests the displacement thickness in this region grows exponentially with time, for certain ranges ofN.For0<N<1,the displacement thickness grows exponentially with time in a manner similar to the non-rotating case. ForN>1,the wall shear remains positive for all time. However, for1⩽N<2,the displacement thickness of the boundary layer close to the rear stagnation point again grows exponentially with time. For2<N<3the flow close to the rear stagnation point also grows exponentially with time, although the form of solution differs from that for0⩽N<2.ForN>3,the solution tends to a truly steady limit, consistent with previous studies on the steady problem. ©1997 American Institute of Physics.