The ornamental design for a round spinning closetorganizer, as shown and described.
FIG. 1 is a perspective view of the round spinning closet organizer of the present invention;
FIG. 2 is a front elevational view thereof;
FIG. 3 is a rear elevational view thereof;
FIG. 4 is a right side view thereof;
FIG. 5 is a left view thereof;
FIG. 6 is top view thereof; and,
FIG. 7 is a bottom view of the present invention.
The hook for holding the closet organizer over a horizontal pole within a closet is shown in dotted lines and forms no part of the claimed invention but is illustrated for environmental purposes, i.e., to show how the device can be hung on a pole in a closet.