# Ball Bearings

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A ball bearing consists of a central cylinder of radius surrounded by tangent balls of radius . All the balls are circumscribed by a hollow cylinder with radius , for simplicity.

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Contributed by: Abraham Gadalla (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Joining the center of the orange disk O to the centers P and Q of two successive purple disks shows that the center angle is , where is the number of purple disks. The line segment connecting O to the tangent point of two consecutive purple disks bisects this angle, so each smaller angle measures . The line segment connecting P and Q is perpendicular to the line segment between the center of the orange disk and the tangent point of the two blue balls. Therefore:

.

Simplifying, .

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