Chapter 10
Center of Gravity
Center of Gravity – Is the point located at the
object’s average position of weight
For symmetrical objects, such as a baseball, the
center of gravity is at the geometric center of the
object.
Consider the following objects and their center of
gravity:
The center of gravity may be located where no actual
material exists:
Q: Where is the center of gravity of a donut?
A: In the center of the hole.
Q: Where is the center of gravity of a basketball?
A: In the center of the basketball.
Q: Can an object have more than one center of gravity?
A: Yes! A rigid object has one CG. If it is nonrigid, such as a
piece of clay or putty, and is distorted into different
shapes, then its CG may change as its shape is changed.
Even then, it has one CG for any given shape.
Center of Mass
The center of gravity is often called center of mass,
which is the average position of all the particles with
mass that make up an object. For almost all objects
on and near the earth. These terms are
interchangeable.
“There can be a small difference
between center of gravity and center of
mass when an object is large enough for
gravity to vary from one part to
another.” For common everyday small
objects, this difference is negligible.
Extrasolar Planets
Here is something VERY cool about center of gravity. You have
always been told that the earth revolves around the sun right?
Well this is not entirely true. The earth and the sun both
revolve around a common center of gravity called the
barycenter. However since the sun is 332,900 times more
massive than the earth, the common center of gravity
between the earth and the sun is located within the sun itself.
As the earth revolves around the sun however, it still causes
our sun to wobble around that point. Astronomers can detect
the wobble of distant stars and can therefore infer the
existance of planets around those stars. As of November 27th,
2012 the extrasolar planet encyclopedia lists 852 extrasolar
planets.
A binary star system:
Common Center of
Gravity
A planetary system:
Common Center of
Gravity
Locating the Center of Gravity
“If you suspend any object (a pendulum, for example) at a single point, the
CG of the object will hang directly below (or at) the point of suspension.”
“You can locate the CG by suspending the object from some other point
and constructing a second vertical line. The CG is where the two lines
intersect.”
Toppling:
“The rule for toppling is this: If the CG of an object is above the area of
support, the object will remain upright. If the CG extends outside the
area of support, the object will topple.” – p. 140
The Leaning Tower of Pisa
Interesting Facts:
Construction: 1173 – 1372
Height: 56.70 meters
Lean: 3.99 degrees
The tower began leaning during
construction, due to the
foundation sinking into the soft
ground beneath the tower.
The tower does not topple over because the center of
gravity is still above its support base.
Unstable equilibrium – any displacement that causes the center
of gravity to be lowered.
Stable equilibrium – any displacement that causes the center of
gravity to rise.
Stable Equilibrium:
Center of Gravity and Potential Energy:
When the CG of an object is raised, potential energy is increased.
When the CG of an object is lowered, the potential energy is decreased.
PE = High
PE = Low