Do you think that punching a punching bag a good way to burn calories in your arms?

Intense burn. Punching a punching bag is an intense upper body workout. The calories burned are burned for your whole body, but the exercise tightens and builds muscles in your arms, shoulders, back and waist. There's some good info here: http://www.Livestrong.Com/article/541231-calories-burned-while-boxing-with-a-heavy-bag/.