The Bucket

LITIn the Scholium to the Definitions of the Principia (1687) Newton hangs a bucket of water from a twisted cord and lets it spin. At first the bucket turns and the water does not: the surface stays flat although the two are in relative motion. Friction slowly drags the water round until both turn together, and the surface rises at the wall into a hollow. Newton read the hollow as a sign of true, absolute rotation, not rotation relative to the bucket.

LIT · MODELA rotating liquid's surface is the paraboloid z = ω²r² / 2g. Here the water's spin relaxes toward the bucket's (viscous coupling), so the hollow emerges in the candlelight; then stop the bucket and the water keeps spinning, hollow, while the bucket is still. For quicksilver the shape is the same (it does not depend on density), which is how liquid-mercury telescope mirrors are made.

spin the bucketstop the bucketliquid: water

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