Single-atomic impurities immersed in a dilute Bose gas in the spherically symmetric harmonic trap potentials are studied at zero temperature. In order to find the ground state of the polarons, we present a conditional variational method with fixed expectation values of the total angular momentum operators,Ĵ 2 andĴ z , of the system, using a cranking gauge-transformation for bosons to move them in the frame co-rotating with the impurity. In the formulation, the expectation value Ĵ2 is shown to be shared in impurity and bosons, but the value Ĵ z is carried by the impurity due to the rotational symmetry. We also analyze the ground-state properties numerically obtained in this variational method for the system of the attractive impurity-boson interaction, and find that excited boson distributions around the impurity overlap largely with impurity's wave function in their quantum-number spaces and also in the real space because of the attractive interaction employed. * Electronic address: b17m6c17m@kochi-u.ac.jp