Center of
Mass

Center of Mass
• A point in the system in which the total mass is concentrated.
• The position of center of mass of a body depends on shape, size
and distribution of mass of the body.
• The center of mass does not lie necessarily at the center of the
body.
• It can be calculated by taking the masses you are trying to find the
center of mass between and multiplying them by their positions

Center of Mass
Wherein:
M = given masses
X = given distances of the masses from origin ; origin = 0

Center of Mass
To determine the location center of mass of two or more masses
lying in horizontal and in vertical axis whose location is relative to
its origin.

Center of Mass
Example:
Consider two masses m= 20 kg and m= 55 kg. If the two masses
are position in x-axis as shown in the figure. Determine the center
of masses.
55 kg 20 kg
5 m
14 m
0

Center of Mass
Example:
An 8 kg mass is placed at y = 3m. Where should a 10 kg mass be
placed axis so that the center of mass will be located at y = 4.5 m?

Center of Mass
1. A 5 kg mass placed at the origin and a 9 kg mass is placed at x =
2 m. Where is the center of the mass?
2. The position of masses 4 kg, 6 kg, 7 kg and 10 kg are (0,0) (4,0)
(0,5) and (5,6) respectively. Determine the position of the center
of mass of the systems?