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A thin wire is bent into the shape of a semicircle $ x^2 + y^2 = 4 $, $ x \geqslant 0 $. If the linear density is a constant $ k $, find the mass and center of mass of the wire.

Mass of the wire is 2$\pi k$ Centre of mass of the wire is $$\left(\frac{4}{\pi}, 0\right)$$

Vector Calculus

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Johns Hopkins University

Harvey Mudd College

University of Michigan - Ann Arbor

Boston College

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