Parts of the clock must be moving for the clock to tick.
closed as not a real question by Manishearth♦ Feb 5 at 14:02
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Indeed, and because many parts of a clock rotate you need to take into account acceleration as well as relative motion (which SR can do - you don't need GR for this).
But since the relative velocities and accelerations are ridiculously small compared to $c$ you would have to be an ubernerd to want to take them into account. As Mitchell says in his comment, you would just take the centre of mass of the clock to define its frame.