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mass motion allows us to make a simplified model of the motion, as if a
complicated object like a human body was just a marble or a point-like
particle. Science really never deals with reality; it deals with models of
reality.
Note that the word “center” in “center of mass” is not meant to imply
that the center of mass must lie at the geometrical center of an object. A car
wheel that has not been balanced properly has a center of mass that does
not coincide with its geometrical center. An object such as the human body
does not even have an obvious geometrical center.
It can be helpful to think of the center of mass as the average location of
all the mass in the object. With this interpretation, we can see for example
that raising your arms above your head raises your center of mass, since the
fixed point on dancer's body
center of mass
A fixed point on the dancer’s body
follows a trajectory that is flatter than
what we expect, creating an illusion
of flight.
center of mass
geometrical
center
An improperly balanced wheel has a
center of mass that is not at its
geometric center. When you get a new
tire, the mechanic clamps little weights
to the rim to balance the wheel.
higher position of the arms’ mass raises the average.
Ballerinas and professional basketball players can create an illusion of
flying horizontally through the air because our brains intuitively expect
them to have rigid-body motion, but the body does not stay rigid while
executing a grand jete or a slam dunk. The legs are low at the beginning
and end of the jump, but come up higher at the middle. Regardless of what
the limbs do, the center of mass will follow the same arc, but the low
position of the legs at the beginning and end means that the torso is higher
compared to the center of mass, while in the middle of the jump it is lower
compared to the center of mass. Our eye follows the motion of the torso
and tries to interpret it as the center-of-mass motion of a rigid body. But
since the torso follows a path that is flatter than we expect, this attempted
interpretation fails, and we experience an illusion that the person is flying
horizontally. Another interesting example from the sports world is the high
jump, in which the jumper’s curved body passes over the bar, but the center
of mass passes under the bar! Here the jumper lowers his legs and upper
body at the peak of the jump in order to bring his waist higher compared to
the center of mass.
Later in this course, we’ll find that there are more fundamental reasons
(based on Newton’s laws of motion) why the center of mass behaves in such
a simple way compared to the other parts of an object. We’re also postpon-
ing any discussion of numerical methods for finding an object’s center of
mass. Until later in the course, we will only deal with the motion of objects’
The high-jumper’s body passes over
the bar, but his center of mass passes
under it.
Photo by Dunia Young.
center
of mass
Chapter 2Velocity and Relative Motion