Moments and Centers of Mass: (Distributed Over a Plane Region)
Given particles of mass distributed over a plane,
Let
Center of One Mass
The Center of One Mass for Each Mass
= (The Displacement From the y-axis , The Displacement From the x-axis)
Moment of One Mass About the x-axis
Moment of One Mass About the x-axis
= (Mass)x(Displacement From the x-axis)
The Moment of One Mass About the y-axis
Moment of One Mass About the y-axis
= (Mass)X(Displacement From the y-axis)
The Mass of the System
Mass of System
= The Sum of All Masses
The Moment of the System About the x-axis
The Moment of the System About the y-axis
The X-Coordinate for the System’s Center of Mass
The Y-Coordinate for the System’s Center of Mass
The system is balanced at the center of mass
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