The Clock Conundrum Question

Hope this makes sense...  A physics teacher of mine stated to the whole class that the outside of a clock-hand moves at greater velocity than the inside and one of the students questioned this by saying something like, if that is the case then why do all parts of the clock-hand make one revolution in the same time. 
He also said that the outside of the clock-hand was not therefor moving at greater velocity, but that it was merely moving with greater angular momentum due to an increase in mass towards the outside and that this makes it seem as though the outside of the hand is going faster but isn't actually the case.
My question is was the teacher correct or the pupil?