387
OF ENGINEERING FOBMULÆ.
Centre of Gravity—continued.
POSITION OF CENTRE OF GRAVITY IN VARIOUS FIGURES.
Parabola ...............= height from base.
Pyramid or cone .. .. = | „
Paraboloid .............= | „
Hemisphere...........= i )t
Segment of circle from) _ Chord3
centre ............J ~ 12 Area
Sector of circle from"! 2 Chord x Rad,
centre ................J ~ 3 Arc
Quadrant sector .. .. = • 6002 Rad.
a circle sector .. .. — • 0366 Rad.
Semicircle .............•= -4244 Rad.
Circular disc ringj_.42„ /R3 - r3\ ,
from centre .. / “ 4244 ( Ü K
and r = radii of outside and inside of ring.
Squares, rectangles, cubes, equilateral triangles,
rings, regular polygons, circles, cylinders, have
their centre of gravity in their geometrical centres.
TO FIND THE CENTRE OF GRAVITY BY EXPERIMENT.
Suspend the body successively in two or more
positions; then the intersection of the vertical
Hues from each point of suspension. will pass
through the centre of gravity.
TO FIND THE COMMON CENTRE OF GRAVITY OF TWO BODIES.
V _= Volume of one body.
v = Volume of the other.
d = Distance of the respective
centres of gravity apart.
X = Distance of common centre of
gravity from centre of gravity
of V.