# Centroid Sentence Examples

- The
**centroid**is at distance 8R from the plane face. - It can be proved by geometry that (aA-H3B) +yC = aA+(aB+- y C) = (a + 1 3+ 7) P, where P is in fact the
**centroid**of masses a, 13, y placed at A, B, C respectively. - This point is the
**centroid**of the body. - The ideas of moment and of
**centroid**are extended to geometrical figures, whether solid, superficial or linear. - The
**centroid**of a figure is a point fixed with regard to the figure, and such that its moment with regard to any plane (or, in the case of a plane area or line, with regard to any line in the plane) is the same as if the whole volume, area or length were concentrated at this point. - The
**centroid**is sometimes called the centre of volume, centre of area, or centre of arc. The proof of the existence of the**centroid**of a figure is the same as the proof of the existence of the centre of gravity of a body. - With regard to a parallel line through the
**centroid**are given by Mi=N1 - xNo=o, M2 = N 2 - 2xN i -{- x 2 No = N2 - x2No, M Q = N Q - g _ 1 q(q 2, I) x 2 Ns -2 - These formulae also hold for converting moments of a solid figure with regard to a plane into moments with regard to a parallel plane through the
**centroid**; x being the distance between the two planes. - A line through the
**centroid**of a plane figure (drawn in the plane of the figure) is a central line, and a plane through the**centroid**of a solid figure is a central plane, of the figure. - The
**centroid**of a rectangle is its centre, i.e. - 0, where S is the area of the revolving figure, and y is the distance of its
**centroid**from the axis. - 0 =L.z.6, where M' is the moment of the original curve with regard to the axis, L is the total length of the original curve, and š is the distance of the
**centroid**of the curve from the axis. - They may be applied, for instance, to finding the
**centroid**of a semicircle or of the arc of a semicircle. - The " central ordinate " is the ordinate through the
**centroid**of the trapezette (§ 32). - The ordinate through the
**centroid**of the figure is the ' ` central ordinate." - In the case, therefore, of any solid whose cross-section at distance x from one end is a quadratic function of x, the position of the crosssection through the
**centroid**is to be found by determining the position of the centre of gravity of particles of masses proportional to So, S2, and 4S 1, placed at the extremities and the middle of a line drawn from one end of the solid to the other. - The
**centroid**of a hemisphere of radius R, for instance, is the same as the**centroid**of particles of masses 0, 7rR 2, and 4.