On the whip see Steven E. Hijmans, Sol: Image and Meaning of the Sun in Roman Art and Religion (Leiden: Brill, 2024), pp. 68-69 (§ 2.7, footnotes omitted):
From the earliest representations in Roman art, a horse-whip (scutica) is a standard attribute of Sol. The scutica typically consists of an arm-length rod to which a single cord, or leather thong, is attached at one end. The whip logically refers to Sol’s role as charioteer of the solar chariot, and as such also occurs when Sol is represented as a standing figure or as a bust. The whip is not unique to Sol, as it is also is an attribute of Luna, but no other deities have a whip as a standard part of their iconography. Thus, when any other male deity is depicted with a whip, this often can be taken as a reference to Sol.This is the only silver coin in my collection, a gift from my son.