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The center of gravity is related
to the center of mass.
All objects are subject to some kind of
torque.
At any
given point in time all objects will have the force of gravity acting on them about their center of mass.
For all intensive purposes the center of mass will be the same as
the center of gravity except when we analyze a body large enough such that the
force of gravity is different in different parts of the object.
Consider that we are on an object (the Earth) that is constantly revolving.
You
will then appreciate the fact that that all objects on this planet have a torque
(t) and
an angular acceleration (a) associated with them.
The
force of gravity
is
acting on them at a certain distance from a fixed point causing a torque.
On Earth, this distance is the radius of gyration from the center of mass of the
Earth to the center of mass of the object.
Complex objects can be analyzed in terms of a center of gravity for the entire object or in terms of individual centers of mass for each component of the object. The total torque on the object will them be equal to the sum of all torques on each of the individual parts of the object.
We can use this concept to arrive at a simple equation used to calculate the location of the center of gravity of a more or less complex object.
Consider the object below. This object is made up of three distinct masses revolving together at the same angular acceleration (a) about a central point C. The radius of rotation (Rcg) is the radius for the total torque (t) acting on the entire object. The mass (m) is made up of the sum of each individual masses m1, m2, and m3.
Note that by inspection, due to the symmetry of the object, we can easily place the center of gravity of the object at the intersection point of the two diagonals inscribed in the object.
We will now locate this center of gravity algebraically.
Let's start by defining the torque, t and the force of gravity Fg, acting on the object:
Example1:
Calculate the center of gravity of the system shown below:
Given:
m1 = 20 Kg m2 = 10 Kg
m3 = 10 Kg m4 = 40 Kg
m5 = 20 Kg
The masses are evenly spaced at 4.0 m apart (center-to-center).
Solution:
[Answer: rcg = 13.2 m]
Example2:
The center of gravity of a 1500 Kg BMW is 3.00 m from the front seat. Where will the cg be located when four passengers (60 Kg each) will occupy the vehicle. Two passenger will seat in the front and two in the back. The front seats are 2.0 m from the front of the car and the back seats are 3.6 m from the front of the car.
Given:
m1 = 1500 Kg
m2 = 2X 60 =120 Kg m3
= 2 X 60 = 120 Kg
r1 = 3.00 m
r2 = 2.0 m
r3 = 3.6 m
Find: rcg
Solution:
= 2.97 m
Also Read about Center of Mass
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