An arm was a body part.
The Tenth Doctor thought it would be "brilliant" to have four arms, as he could do everything he normally did with only two of them, and still have a pair of arms free for some knitting. (AUDIO: Infamy of the Zaross)
According to Faction Paradox legend, Grandfather Paradox had only one arm. (PROSE: The Gallifrey Chronicles) A future version of the Eighth Doctor whose biodata had been corrupted by the Faction modelled himself as Grandfather Paradox, including removing one of his arms. This also may have been because he knew it was the arm which the Doctor would use to destroy Gallifrey. (PROSE: The Ancestor Cell)
The Ninth Doctor pulled off the plastic arm of an Auton when it came between the doors of a lift he and Rose Tyler were using to escape them in Henrik's. Left with the arm, Rose took it back home to the Powell Estate where it was picked up and thrown in the bin by Mickey Smith. On the following day, it was animated by the Nestene Consciousness and, making its way back through the cat flap, proceeded to attack the Doctor then Rose before the Doctor used the sonic screwdriver to sever the Nestene signal, rendering it "armless". He found that the arm was too "simple" to be used to trace the Nestene Consciousness. (TV: Rose)