Help Please

[jellybean]

calculate the moments M(with subscript x) and M(with subscript y) and the center of mass of a lamina with the given density and shape.


density=2

Not good at posting pictures so i will explain

the shape is in the first quadrant of a graph. its a quarter-circle. the two main points that connect the arc of the quarter-circle are (0, r) and (r, 0).[/img]

 

[TchrWill]

calculate the moments M(with subscript x) and M(with subscript y) and the center of mass of a lamina with the given density and shape.
density=2
the shape is in the first quadrant of a graph. its a quarter-circle. the two main points that connect the arc of the quarter-circle are (0, r) and (r, 0).[/img]

The centroid of a quarter circle is x = 2Rsinµ/3µ, R being the radius and µ the half angle of the sector being 45º. This centroidal distance, x, frpm the apex of the sector is measured along the line bisecting the sector.

The distance from the y axis to the centroid measured parallel to the x axis and the same disance measured parallel to the y axis is xcos45º = .707x.

You can calculate the area of the quarter circle from A(1/4) = PiR^2/4.

he mass of the slab is then 2PiR^2/4 = PiR^2/2.

Having both distances from the x and y axes and the mass, you can now compute the moment of the slab about both axes which will be equal to one another..