Center of Gravity RIGID BODY PARAMETERS Center of Gravity Machinery's Handbook, 31st Edition
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The center of gravity of a body, volume, area, or line is that point at which if the body, volume, area, or line were suspended it would be perfectly balanced in all positions. For symmetrical bodies of uniform material it is at the geometric center. The center of grav- ity of a uniform round rod, for example, is at the center of its diameter halfway along its length; the center of gravity of a sphere is at the center of the sphere. For solids, areas, and arcs that are not symmetrical, the determination of the center of gravity may be made experimentally or may be calculated by the use of formulas. The tables that follow give such formulas for some of the more important shapes. For more complicated and unsymmetrical shapes the methods outlined on page 234 may be used. Example: A piece of wire is bent into the form of a semi-circular arc of 10-inch (25.4 cm) radius. How far from the center of the arc is the center of gravity located? Solution: Accompanying the Circular Arc diagram on page 229 is a formula for the distance from the center of gravity of an arc to the center of the arc: a = 2 r ÷ π . Therefore, . . . . . a a 31416 2 10 6366 31416 2 254 1617 inches cm # # = = = = Formulas for Center of Gravity Triangle:
Perimeter If A , B and C are the midpoints of the sides of the triangle, then the center of gravity is at the center of the circle that can be inscribed in triangle ABC . The distance d of the center of gravity from side a is: d a b c h b c 2 = + + + ^ ^ h h where h is the height perpendicular to a . Area The center of gravity is at the intersection of lines AD and BE , which bisect the sides BC and AC . The perpendicular distance from the center of gravity to any one of the sides is equal to one-third the height perpendicular to that side. Hence, a = h ÷ 3.
B
C
b
h
c
h
A
a
A
E
h
a
D C
B
Perimeter or Area of a Parallelogram:
The center of gravity is at the intersection of the diagonals.
C
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