# Center of Mass Formula

The center of mass is a point of balance of an object or a group of objects. The center of mass can be found for any one, two-, or three-dimensional object, and so the units are meters (*m*) in each dimension. The formula given here is for the center of mass in one dimension.

*X* = center of mass (*m*)

*m _{i}* = mass of a part of an object (

*kg*)

*x _{i}* = position of the part of an object (

*m*)

Center of Mass Formula Questions:

1) The minute hand of a clock consists of an arrow and a circle connected by a thin piece of metal with negligible mass. The arrow has a mass of 15.0 *g*, and the circle has a mass of 60.0 *g*. If the circle is at position 0.000 *m*, and the arrow is at position 0.100 *m*, where is the center of mass?

Answer: The center of mass of the minute hand can be found using the formula:

X = 0.020 *m*

The center of mass is 0.020 *m* from the circle.

2) A hanging light fixture has the following lights attached to it: i) a 0.10 *kg* light at position 0.00 *m*, ii) a 0.20 *kg* light at position 0.20 *m*, iii) a 0.80 *kg* light at position 0.80 *m*, and iv) a 0.10 *kg* light at position 1.0 *m*. Where is the center of mass?

Answer: The center of mass of the minute hand can be found using the formula:

X = 0.65 *m*

The center of mass is at position 0.65 *m*.

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