We investigate the dynamics of strongly localized solitons trapped in remote troughs of radially periodic lattices with Kerr-type self-focusing nonlinearity. The rotary motion of solitons is found to be more stable for larger nonlinear wavenumbers, lower rotating velocity, and shorter radius of the trapping troughs. When the lattice is shrunk or expanded upon propagation, the solitons can be trapped in the original trough and move outward or inward, with their rotating linear velocity inversely proportional to the radius of the trapping troughs.