For every system and at every instant in time, there is a unique location in space that
is the average position of the system’s mass. This place is called the center of mass,
commonly designated by cm, c.o.m., COM, G, c.g., or .
One of the routine but important tasks of many real engineers is to find the center
of mass of a complex machine1 . Just knowing the location of the center of mass of 1 Nowadays this routine work is often
done with CAD (computer aided design)
software. But an engineer still needs to
know the basic calculation skills, to make
sanity checks on computer calculations if
nothing else.
a car, for example, is enough to estimate whether it can be tipped over by maneuvers
on level ground. The center of mass of a boat must be low enough for the boat to be
stable. Any propulsive force on a space craft must be directed towards the center of
mass in order to not induce rotations. Tracking the trajectory of the center of mass of
an exploding plane can determine whether or not it was hit by a massive object. Any
rotating piece of machinery must have its center of mass on the axis of rotation if it
is not to cause much vibration.
Also, many calculations in mechanics are greatly simplified by making use of a
system’s center of mass. In particular, the whole complicated distribution of nearearth
gravity forces on a body is equivalent to a single force at the body’s center of
mass. Many of the important quantities in dynamics are similarly simplified using
the center of mass.