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320 CHAPTER 10 Systems of Particles

PROBLEM-SOLVING TECHNIQUES CENTER OF MASS

Calculations of the position of the center of mass of a body For instance, in the example of the bent meterstick, it is
can often be simplified by exploiting the shape or the sym- obvious that the center of mass of each half is at its center.
metry of the body.
• Geometrical arguments can sometimes replace algebraic
• Sometimes it is profitable to treat the body as consisting calculations of the coordinates of the center of mass. For
of several parts and to begin by calculating the positions instance, in the example of the bent meterstick, instead
of the centers of mass of these parts (as in the example of of the algebraic calculations of the coordinates [such as
the bent meterstick). Each part can then be treated as a for x CM in Eq. (10.28)], the coordinates can be obtained
particle located at its center of mass, and the center of by regarding the stick as consisting of two straight pieces
mass of the entire body is then the center of mass of this with known centers of mass; then the coordinates of the
system of particles, which can be calculated by the sums, overall center of mass can be found from the geometry
Eqs. (10.18)–(10.20). of a diagram, such as Fig. 10.12.
• If the body or some part of it has symmetry, the position
of the center of mass will often be obvious by inspection.

PHYSICS IN PRACTICE CENTER OF MASS AND STABILITY

In the design of ships, engineers need to ensure that the posi- voyage when struck by a gust of wind, just barely out of harbor.
tion of the center of mass is low in the ship, to enhance the It carried an excessive number of heavy guns on its upper
stability. If the center of mass is high, the ship is top-heavy and decks, which made it top-heavy; and it should have carried
liable to tip over. Ships often carry ballast at the bottom of more ballast to lower its center of mass.
the hull to lower the center of mass. Many ships have been lost The position of the center of mass is also crucial in the
because of insufficient ballast or because of an unexpected design of automobiles. A top-heavy automobile, such as an
shifting of the ballast. For instance, in 1628, the Swedish ship SUV, will tend to roll over when speeding around a sharp
Vasa (see Fig. 1), the pride and joy of the Swedish navy and curve. High-performance automobiles, such as the Maserati
King Gustavus II Adolphus, capsized and sank on its maiden shown in Fig. 2, have a very low profile, with the engine and
transmission slung low in the body, so the center of mass is as
low as possible and the automobile hugs the ground.

FIG. 1 The Swedish ship Vasa. FIG. 2 A Maserati sports car.