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.
Center of mass = (m1x1y1 + m2x2y2 + … + mNrN) / (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 the point masses by each coordinate, add these values together, then divide by the sum of the point masses.
Center of Mass Definition
The center of mass is defined as the point in which if all of the mass of an object was located at that single point, it would behave the same way as the true body of the mass.
Center of Mass Example
How to calculate a center of mass
- First, measure all of the individual point masses
In this case, it’s extremely important that the masses you are using can be modeled as point masses. If they were irregular objects, this formula would not hold.
- Next, measure the distance of each mass
Measure the distance of each mass from an origin of x=0 and y=0
- Calculate the center of mass
Calculate the center of mass using the formula above and the measured values from steps 1 & 2.
A center of mass is a term used in physics to describe a single point location that could be used in order to model where a mass of an object was located if all of that mass of the individual object was located at one discrete point.
A point mass is a single point in which mass is located.