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How Does Time Dilation Work for a Mechanical Clock?

how does time dilation work for a mechanical clock

I understand that time dilation is when the gravitational pull will change the distance the speed of light is traveling. However, how would this work for a mechanical clock? Say the arms of the clock act as the speed of light and it sits on a strong gravitational pull. Since the arms travel in a circle it would be faster going from the 12 spot to the 6 (since it is moving toward the pull) but slower going from the 6 to the 12 (since it is moving away from pull)? Therefore, evening itself out and there would be no time change, right?

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