Why does the axis of rotation pass through the metacentre?

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The discussion centers on the concept of the metacentre in relation to a ship's axis of rotation when it heels. It explains that the center of buoyancy shifts laterally and potentially vertically, with the metacentre defined as the intersection of vertical lines from the heeled and original centers of buoyancy. There is skepticism about whether the metacentre is indeed the point around which a ship rotates during small angular displacements. The argument suggests that the center of rotation is typically near the waterline, while the metacentre is perceived to be above it. The conversation concludes with an acknowledgment of the differing viewpoints on this topic.
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When a ship heels, the centre of buoyancy of the ship moves laterally. It might also move up or down with respect to the water line. The point at which a vertical line through the heeled centre of buoyancy crosses the line through the original, vertical centre of buoyancy is called the metacentre. But how can we prove that point, about which the ship rotates (starts oscillating for the small angular displacements), is the metacentre?
 
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I don’t think it is. When a ship heels, the center of rotation is usually near the waterline. The metacentre, based on your description, sounds like it would always be above the waterline.
 
LURCH said:
I don’t think it is. When a ship heels, the center of rotation is usually near the waterline. The metacentre, based on your description, sounds like it would always be above the waterline.
Thank you. You are right
 

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