We have used the polar cap (PC) index, which is a measure of magnetic disturbance caused by the transpolar portion of ionospheric currents associated with global convection, to investigate the effect of sudden changes in the solar wind dynamic pressure (PSW). We find that during a period of steady interplanetary magnetic field (IMF), the PC index shows an enhancement that is a direct response to an enhancement in PSW. Examination of the response associated with the passage of interplanetary clouds accompanied by magnetic storms shows that a PSW pulse can cause changes in the PC index that are as large as the effects due to the changes in the interplanetary electric field. Responses of the PC index, AE index, and low-latitude horizontal component of magnetic field are observed to be similar, though during a magnetic storm, the influence of a significant ring current can distort the dayside low-latitude response. Sudden increases in PSW lead to an initial negative spike in the PC index that is followed by the main increase. Sudden decreases in PSW are found to have the opposite effect: an initial positive spike that is followed by a decrease in the PC index. The spike of ~3 min duration is found to initiate simultaneously with the sudden impulse or commencement and an AE spike on the ground and the same time that geosynchronous particle fluxes start to increase sharply in response to magnetic field compression. It likely reflects a temporal response of convection to an abrupt change in PSW that is initially of the opposite sign to the more prolonged response, and it may be associated with short time scale current vortices that have been observed in the ionosphere near noon. The above results show that both PSW and IMF play a significant role in controlling the strength of magnetospheric convection.