Enter the x and y dimensions and masses of up to 5 individual points into the calculator. The calculator will determine the center of mass of the masses entered.
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Center of Mass Formula
The following formula is used to calculate a center of mass of multiple point masses.
For point masses in 2D, compute each coordinate separately:
xcm = (m1x1 + m2x2 + … + mNxN) / (m1 + m2 + … + mN)
ycm = (m1y1 + m2y2 + … + mNyN) / (m1 + m2 + … + mN)
- Where m is the mass of each point
- x is the coordinate distance of each point along the x-axis
- y is the coordinate distance of each point along the y-axis
To calculate a center of mass, multiply each point mass by its coordinate, add these values together, then divide by the sum of the point masses. Do this separately for the x-coordinate and y-coordinate.
Center of Mass Definition
The center of mass is the mass-weighted average position of an object or system of objects. In many problems (for example, translational motion under uniform gravity), the system behaves as if all its mass were concentrated at this point.
Center of Mass Example
FAQ
A center of mass is the mass-weighted average position of an object or system. It is a single point that can be used to model the system’s translational motion (for example, under uniform gravity) as if the mass were concentrated there.
A point mass is an idealized model in which an object’s size is negligible compared with the distances involved, so its mass can be treated as concentrated at a single point.
