Two ways that I can tell is that rusting is a chemical reaction because it is not caused by any physical force or trauma it's oxidation and it changes colors from heat and heat is one of the main factors for a chemical reaction.
Touching the battery to steel wool sends a current through the thin wire, and it heats up a lot (to about 700 degrees C). These temperatures cause the iron to react with the oxygen (O2) in the air and creates iron oxide (FeO2).
