The boundary of a thin plate is an ellipse with semiaxes a and b.

Let L denote a line in the plane of the plate passing through the center of the ellipse and making an angle k with the axis of length 2a

If the density is constant and if the mass of the plate is m,

find out the moment of inertia about line L.

I tried to find out the perpendicular distance from point in L to point in boundary since moment of inertia is double integrate the product of square of distance from L to Boundary and density.

What is the equation for perpendicular distance for this ?

  • $\begingroup$ If the centre is on the x axis at the origin you could consider what happens to the equation of the ellipse if it's rotated. L could then be treated as being on the x axis. $\endgroup$ – user117644 Mar 29 '15 at 7:30
  • $\begingroup$ could you explain more please..? $\endgroup$ – Nancy Mar 30 '15 at 2:42
  • $\begingroup$ maa.org/external_archive/joma/Volume8/Kalman/General.html You won't need to translate, just rotate. If L is on the x axis, y will be the perpendicular distance. $\endgroup$ – user117644 Mar 30 '15 at 7:32

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