What is Center of Mass ?

Center of Mass that point where the entire mass of body is assumed to be concentrated ” or ” It is that point where the entire mass of a body balances itself “.

Now, before understanding center of mass of a triangle first understand the concept using a simpler example.

Let us understand this with an example of a rod. As you can see a rod we have a rod in the image below . Now I can pick this rod my holding the entire rod in my hand and then just lift this rod. However, there is an other way of how I can pick this up. That is by applying the same force on the exact middle which is pointed by the arrow in the figure below. That point is the center of Mass of this Rod.

center of mass of rod

Center of Mass of a Triangle

Now, Similarly the Center of mass of a triangle lies exactly at the geometric center of the Triangle. That is if we have an equilateral triangle then the center of mass of the triangle lies exactly at a height of 1/3 times height from any Base.

center of mass of triangle

In the above figure if the height of this triangle is h then the center of mass lies at a height h/3 from base as shown in the figure.

Now let us understand how we can calculate center of mass for triangles with unequal sides. There are basically Two methods we will Discuss then understand the same using some examples.

Method 1 : Using the Method Intersecting Medians

The center of mass can be calculated by finding the intersection of any two medians of the triangle . There are certain steps involved in the calculation process .

center of mass of triangle calculation

Step 1 : Calculate the Length of any two sides of the Triangle

In the above example the length of the two sides of the triangle are taken as 8m and 6m respectively.

Step 2 : Calculate the mid point of each of the side

Once we are done with measuring the length of each of the side. Now, we need to find the midpoint of each side. I can be calculated by dividing the length of the side by 2.

Therefore , 8/2 and 6/2 gives 4,3 . So Mark a point at the length 4 ( point A in figure ) and 3 ( point B in figure ) on the sides respectively.

Step 3 : Drawing Medians from these midpoints to the opposite vertex

The next step is to draw the median from this midpoint to the opposite vertex . In the figure lines are drawn from the midpoints A and B to the opposite vertices as shown in the figure.

Step 4 : Marking the point of intersection of the diagonals

The point of intersection of the diagonals gives the location of the center of mass.

Method 2 : By Dividing Median in the ratio of 1:2

In this method we choose any one of the median and then divide that in the ratio of 1:2. And then Locate the center of mass. The steps to find are as stated below.

center of mass of triangle calculation

Step 1 : Draw any one median

A median is a straight line joins the center of any one of the side with the vertex opposite to it.

Step 2 : Dividing the Median in the ratio 1:2

The next step is to divide the line is the ratio of 1:2 from the midpoint to the opposite vertex and Mark that point.

Step 3 : Locate the center of mass

The marked point represents the center of mass and the distance of center of mass from the base is the distance between the mid point and the vertex.

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