centre of mass of half-disc

Let E be the upper half-disc of the disc  x2+y2R  in 2 with a surface-density 1. By the symmetry, its centre of mass lies on its medium radius, and therefore we only have to calculate the ordinate Y of the centre of mass. For doing that, one can use the double integral


where  ν(E)=πR22  is the area of the half-disc. The region of integration is defined by

E={(x,y)2-RxR, 0yR2-x2}.

Accordingly we may write


Thus the centre of mass is the point  (0,4R3π).

Title centre of mass of half-disc
Canonical name CentreOfMassOfHalfdisc
Date of creation 2013-03-22 17:20:57
Last modified on 2013-03-22 17:20:57
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 10
Author pahio (2872)
Entry type Example
Classification msc 28A75
Classification msc 26B15
Synonym center of mass of half-disc
Synonym centroid of half-disc
Related topic SubstitutionNotation
Related topic CentreOfMassOfPolygon
Related topic CenterOfGravityOfCircularSector
Related topic AreaOfSphericalZone