|
|
Center of Mass for Planar Region in Polar Coordinates
|
|
|
|
Description
|
|
Determine  and  , the center of mass coordinates for a planar region in polar coordinates.
|
|
Center of Mass for Planar Region in Polar Coordinates
|
|
Density:
|
|
>
|
|
|
| (1) |
|
|
Region:  <= r and r <= r[2](theta)}](/support/helpjp/helpview.aspx?si=3995/file05228/math73.png)
|
|
](/support/helpjp/helpview.aspx?si=3995/file05228/math80.png)
|
|
>
|
|
|
| (2) |
|
|
](/support/helpjp/helpview.aspx?si=3995/file05228/math96.png)
|
|
>
|
|
|
| (3) |
|
|
|
|
>
|
|
|
| (4) |
|
|
|
|
>
|
|
|
| (5) |
|
|
Moments Mass:
Inert Integral - 
|
|
>
|
![Student[MultivariateCalculus][CenterOfMass](__r__, __r__ = 0 .. 1, theta = 0 .. (1/2)*Pi, coordinates = polar[__r__, theta], output = integral)](/support/helpjp/helpview.aspx?si=3995/file05228/math158.png)
|
|
| (6) |
|
|
Explicit values for  and 
|
|
>
|
![Student[MultivariateCalculus][CenterOfMass](__r__, __r__ = 0 .. 1, theta = 0 .. (1/2)*Pi, coordinates = polar[__r__, theta])](/support/helpjp/helpview.aspx?si=3995/file05228/math177.png)
|
|
| (7) |
|
|
Plot:
|
|
>
|
![Student[MultivariateCalculus][CenterOfMass](__r__, __r__ = 0 .. 1, theta = 0 .. (1/2)*Pi, coordinates = polar[__r__, theta], output = plot, caption = "")](/support/helpjp/helpview.aspx?si=3995/file05228/math193.png)
|
|
|
|
|
|
Download Help Document
Was this information helpful?
