An elementary treatise on theoretical mechanics (1893)
Ziwet, Alexander, 1853-1928 · New York, London, Macmillan and Co. · leaf 31
radius a, in which the density varies directlyas the distance from the centre (Fig. 9). Let a circle describedupon a radius as diameter be cut out of this disc; it is requiredto find the centroid of the remainder. Let O be the centre of the disc of radius a, C that of thedisc of radius \a; G^ the… … Fig. 9. The equation of the smaller circle is r=acosd. Taking aselement of the mass of the smaller disc the mass containedbetween two arcs of radii ^and r+dr, we have for this element: dM^=p-2drdr, or since p = kr, r=a cos 0, dMj^=2 Jta^d cos^0d (cos 9). Hence M^=lkc^^led (cos¥) =%ka^U cos¥…
Mechanics, Analytic
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