# Center of Mass

Discussion in 'Physics' started by Lightfire, Oct 27, 2012.

1. ### Lightfire Thread Starter Well-Known Member

Oct 5, 2010
690
21
Hello,

I find this very fascinating. I read somewhere that car manufactures uses the principle of center of mass (Or maybe center of gravity, I do not know if they are the same) .

From Wikipedia,

In physics, the center of mass, or barycenter, of a distribution of mass in space is the unique point where the weighted relative position of the distributed mass sums to zero.

Questions? What is relative position?

Another one,

In the case of a single rigid body, the center of mass is fixed in relation to the body, and if the body has uniform density, it will be located at the centroid.

So what is uniform density?

Sorry for these questions. Ok? I just want to play like this man.

I can't resize the photo. sorry.

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2. ### MrChips Moderator

Oct 2, 2009
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5,328
Center of mass and center of gravity are not the same.

In outer space where there is no significantly large body to exert gravitational force, there is no center of gravity. Hence it is more appropriate to talk about center of mass.

On planet Earth, if gravity is applied uniformly, then the location of center of mass will coincide with the center of gravity.

Relative position is the position of a point mass with respect to any arbitrary point.

Here is an example. Assume you have different masses on an imaginary rod separated by different distances as shown:

You can choose any arbitrary Reference Point. The relative positions of the mass are x1, x2, x3 and x4

In this simple example, if the masses are equal and equally spaced, we can say that the masses are uniformly distributed and therefore have uniform density.

In the simple one-dimensional example I have shown you can determine the center of mass as follows.

The moment of mass for a single mass is the product of the mass and its relative position, i.e. m1 . x1

To calculate the total moment of mass, we add all the individual moments of mass:

$Total Moment Of Mass = (m1 \cdot x1) + (m2 \cdot x2) + (m3 \cdot x3) + (m4 \cdot x4)$

We can write this in the general form as:

$Total Moment Of Mass = \sum m_i \cdot x_i$

We calculate the total mass as:

Total Mass = m1 + m2 + m3 + m4

or

$Total Mass = \sum m_i$

From these two, we can determine the relative position of the center of mass:

Center of Mass = (Total Moment of Mass)/(Total Mass)

$Center Of Mass = \frac{\sum m_i \cdot x_i }{\sum m_i}$

I have shown you the simple case for a one-dimensional object.
You apply the same formulas for two or three dimensional objects, calculating the center of mass in the x, y and z directions separately.

Last edited: Oct 27, 2012
3. ### MrChips Moderator

Oct 2, 2009
17,296
5,328
Your picture of balancing the bird on its beak is having simple knowledge of physics.

The center of gravity has to be below the the tip of the beak or the tip of the tooth pick.

If the center of gravity is higher, the object is unbalanced and will fall over.

When the center of gravity is lower, the object is self stabilizing.

4. ### atferrari AAC Fanatic!

Jan 6, 2004
3,059
1,139
Look a these as well

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