There are several synonyms for the word "cartwheeling." One common option is "somersaulting," which refers to the acrobatic move of flipping forward or backward while tucking the head and rolling over the shoulders. Another synonym is "wheeling," which often refers to a circular motion or rotation. A third option is "flipping," which could refer to any kind of acrobatic or gymnastic movement that involves turning one's body over in the air. Other possible synonyms might include "rolling," "tumbling," or "gyrating," depending on the specific context and connotations of the word. Ultimately, the right synonym for "cartwheeling" will depend on the nuances of the sentence and the author's intent.