# Physics Tutorial 6.2 - Determining the Centre of Mass in Objects and Systems of Objects Revision Notes

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6.2Determining the Centre of Mass in Objects and Systems of Objects

In these revision notes for Determining the Centre of Mass in Objects and Systems of Objects, we cover the following key points:

• How to determine the centre of mass position for a non-homogenous object
• The same for a system of collinear distant objects
• How to find the centre of mass of a system composed by three or more objects using coordinates

## Determining the Centre of Mass in Objects and Systems of Objects Revision Notes

Centre of mass of a regular non-homogenous object is determined by taking each homogenous part as a separate object and then applying the equation

xC = x1 × m1 + x2 × m2 + …/m1 + m2 + …
yC = y1 × m1 + y2 × m2 + …/m1 + m2 + …
zC = z1 × m1 + z2 × m2 + …/m1 + m2 + …

where x1, x2, y1, y2, z1, z2 etc., are the coordinates of centres of mass for each single regular part of the object or system and m1, m2, etc are their respective masses.

In one dimension (in a straight line), we use only the x-coordinates, in two dimensions (in a plane) we use both x and y-coordinates and in three dimensions (in space) we use all three coordinates.

If there is a system composed by two or more distant objects, we can use a similar procedure for calculating its centre of mass if the individual masses and positions (coordinates) of each object are known. Even when the objects are irregularly shaped, we can ignore their shape and concentrate only on their respective centres of mass.

Despite the objects are distant, we consider them as a single system of objects connected through very light sticks whose masses are neglected.

It is not important where you take the origin when calculating the centre of mass of a system of objects as long as you make the calculations correctly.

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