Moments and Centers of Mass: (Bounded by Two Curves)
Using Vertical Strips
Given two functions y= f(x) and y = g(x) from x= a to x= b, the center of mass bounded by two curves can be found using vertical strips.
When using vertical strips, functions of x are written and integrated with respect to x.
Let
Center of Mass for One Strip
Dimensions of One Strip
Area of One Strip
Area of One Strip
= (Length)x(Width)
Mass of One Strip
Mass of One Strip
= (Density)X(Area)
Moment of One Strip About the x-axis
Moment of One Strip About the x-axis
= (Mass)X(Displacement From the x-axis)
Moment of One Strip About the y-axis
Moment of One Strip About the y-axis
= (Mass)X(Displacement from the y-axis)
Area of System
Area of System
= The Sum of all Areas
Mass of System
Mass of System
= The Sum of all Masses
Moment of System About the x-axis
Moment of system about the x-axis
= the sum of all moments about the x-axis
Moment of System About the y-axis
Moment of System About the y-axis
= The Sum of All Moments About the y-axis
Center of Mass of System
The system is balanced at the center of mass
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