The center of mass is the point located in an average position concerning the objects' positions and their masses. (a/3;a/3) is the location of the COM.
The center of masses of a given system of particles or objects is the position under which all external forces are acting. Any uniform force acts on this point.
This position is the average position of all the components of the system concerning their masses. It can be placed in one, two or three dimensions according to the system.
Coordinate X of the center of masses is given by the following formula,
Xcom = Σ(Ximi) / Σmi
This is the adition (Σ) of each particle position on the X-axis (Xi) multiplied by their mass (mi), and the result divided by the summation of all masses -total mass-.
In the same way, coordinate Y of the center of masses is given by the following formula,
Ycom = Σ(Yimi) / Σmi
This is the adition (Σ) of each particle position on the Y-axis (Yi) multiplied by their mass (mi), and the result is divided by the summation of all masses.
The center of masses is located in the position (X, Y).
According to this framework, we can get the coordinates of the center of masses for this bidimensional system. Coordinates can be expressed in meters or centimeters (m or cm).
Data:
Particle ⇒ (X;Y)
Coordinate X ⇒ Xcom = Σ(Ximi) / Σmi
Xcom = (0m) + (0m) +(am) / m +m +m
Xcom = am / 3m
Xcom = a/3
Coordinate Y ⇒ Ycom = Σ(Yimi) / Σmi
Ycom = (am) + (0m) +(0m) / m +m +m
Ycom = am / 3m
Ycom = a/3
Coordinates of the center of masses, (X;Y) = (a/3 ; a/3)
(a/3 ; a/3) is the location of the center of mass in the proposed bidimensional system.
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