Thank you for an interesting post, @Ocatarinetabellatchitchix . Here’s one—I think the charioteer is holding a crop or a whip. When I was in high school I owned a braided leather whip. I became quite adept at being able target tin cans that I would set up and producing a loud crack sound.
Interesting post again @Ocatarinetabellatchitchix. Here's an interesting excerpt from Cicero's in Verrem, perhaps fitting with your post: facinus est vincire civem Romanum, scelus verberare, prope parricidium necare: quid dicam in crucem tollere? Verbo satis digno tam nefaria res appellari nullo modo potest. It is a crime to bind a Roman citizen; to flog him is a wickedness; to put him to death is almost parricide. What shall I say of crucifying him? So guilty an action cannot by any possibility be adequately expressed by any name bad enough for it. Uncertain if the whip referred to here, is the flagrum shown by you. The same can be said for my coin, that shows a 'whip' (or is it a stick?). I doubt it is a flagrum though.