For the dominant limb, a velocity-dependent change in rotational axes during the kinesthetic control of unconstrained 3D arm rotations was reported, and thus the question arises if this can be reproduced for the nondominant arm. The rotation axes considered are the axes of minimum inertia (e3), the shoulder-center of mass axis (SH-CM), and the shoulder-elbow axis (SH-EL). The objective of this study was to examine whether the minimum inertia axis would constrain internal-external rotations of the shoulder at fast velocity. Participants performed cyclic rotations of their arms in 2 sensory conditions and at 2 velocities. The elbow configurations were either set to 90° or 140° to yield a constant separation between e3, SH-CM, and SH-EL. Our results showed that the limb's rotational axis coincide with the SH-EL axis across velocity conditions, although higher variability was seen at higher velocity. This was true for both the dominant and the nondominant arm. Together, the results showed that cognitive instruction prevented a velocity-dependent rotation axis change toward e3 and/or SH-CM, as proposed in the minimum inertia principle.