## Centre of Mass of a Solid of Revolution

When a curveis rotated about the- axis, the centre of mass of the solid generated will line on the– axis because of the symmetry of the curve. The centre of mass will not lie on the– axis however.

If the centre of gravity of a volume of revolution of massis at then taking moments about the- axis for the section of solid of thicknessof radiusgives a mass for this section ofso lettingintegrating and equating to the moment of the whole solid gives

Similarly the centre of mass of the solid of revolution for a curverotated about the- axis iswhere

Example: Find the centre of gravity of the solid of revolution formed bybetweenand