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10.2 Center of Mass 313

✔ Checkup 10.1

QUESTION 1: An automobile and a truck have equal momenta. Which has the larger
speed? Which has the larger kinetic energy?
QUESTION 2: An automobile and a truck are traveling along a street in opposite direc-
tions. Can they have the same momentum? The same kinetic energy?
QUESTION 3: A rubber ball, dropped on a concrete floor, bounces up with reversed
velocity. Is the momentum before the impact the same as after the impact?
QUESTION 4: Is the net momentum of the Sun and all the planets and moons of the
Solar System constant? Is the net kinetic energy constant?
QUESTION 5: Consider two automobiles of equal masses m and equal speeds v. (a) If
both automobiles are moving southward on a street, what are the total kinetic energy
and the total momentum of this system of two automobiles? (b) If one automobile is
moving southward and one northward? (c) If one automobile is moving southward
and one eastward?
QUESTION 6: An automobile and a truck have equal kinetic energies. Which has the
larger speed? Which has the larger momentum? Assume that the truck has the larger
mass.
(A) Truck; truck (B) Truck; automobile
(C) Automobile; truck (D) Automobile; automobile

10.2 CENTER OF MASS

In our study of kinematics and dynamics in the preceding chapters we always ignored
the size of the bodies; even when analyzing the motion of a large body—an automo-
bile or a ship—we pretended that the motion could be treated as particle motion, posi-
tion being described by means of some reference point marked on the body. In reality,
large bodies are systems of particles, and their motion obeys Eq. (10.13) for a system
of particles. This equation can be converted into an equation of motion containing
just one acceleration rather than the rate of change of momentum of the entire system,
by taking as reference point the center of mass of the body.The equation that describes center of mass
the motion of this special point has the same mathematical form as the equation of
motion of a particle; that is, the motion of the center of mass mimics particle motion
(see, for example, Fig. 10.6).

Strobe light records Although wrench spins,
images at equal the center of mass
time intervals. moves uniformly.

FIGURE 10.6 A wrench moving freely in
the absence of external forces. The center of
mass, marked with a dot, moves with uni-
form velocity, along a straight line (you can
check this by laying a ruler along the dots).