Chapter 2 Review of Forces and Moments - Brown University

TABLE OF POSITIONS OF CENTER OF MASS FOR COMMON OBJECTS
Rectangular prism Circular cylinder Half-cylinder
Solid hemisphere Thin hemispherical shell Cone
Triangular Prism
Thin triangular laminate
Some subtleties about gravitational interactions
There are some situations where the simple equations in the preceding section don’t work. Surveyors
know perfectly well that the earth is no-where near spherical; its density is also not uniform. The earth’s
gravitational field can be quite severely distorted near large mountains, for example. So using the simple
gravitational formulas in surveying applications (e.g. to find the `vertical’ direction) can lead to large
errors.
Also, the center of gravity of an object is not the same as its center of mass. Gravity is actually a
distributed force. When two nearby objects exert a gravitational force on each other, every point in one
body is attracted towards every point inside its neighbor. The distributed force can be replaced by a
single, statically equivalent force, but the point where the equivalent force acts depends on the relative
positions of the two objects, and is not generally a fixed point in either solid. One consequence of this
behavior is that gravity can cause rotational accelerations, as well as linear accelerations. For example,
the resultant force of gravity exerted on the earth by the sun and moon does not act at the center of mass
of the earth. As a result, the earth precesses – that is to say, its axis of rotation changes with time.