Using a multilayer containing a cobalt detector layer, a copper spacer, and a Permalloy source layer, we show experimentally how the nonreorientable spin-orbit torque generated by the Permalloy source layer - the component of spin-orbit torque that does not change when the Permalloy magnetization is rotated - can be measured using spin-torque ferromagnetic resonance (ST FMR) with line-shape analysis. We find that dynamic spin pumping between the magnetic layers exerts torques on the magnetic layers as large as, or larger than, the spin-orbit torques, so that if dynamic spin pumping is neglected, the result will be a large overestimate of the spin-orbit torque. Nevertheless, the two effects can be separated by performing ST FMR as a function of the frequency. We measure a nonreorientable spin torque ratio ζDL=0.04±0.01 for the spin-current flow from Permalloy through an 8-nm Cu spacer to the Co and a strength of dynamic spin pumping that is consistent with previous measurements by conventional ferromagnetic resonance. © 2021 American Physical Society.