Moment of inertia uniform plate problem

[monotonousJ]

My homework problem goes like this:
A uniform plate of height H = 1.39 m is cut in the form of a parabolic section. The lower boundary of the plate is defined by: y = 0.25 x2. The plate has a mass of 4.67 kg. Find the moment of inertia of the plate (in kgm2) about the y-axis.

I know I=int(r^2)dm, but I don't know really how to apply it to this problem.
I need some help getting started, or even some info on calculating moments of inertia of random objects. Thank you.

 

[OlderDan]

My homework problem goes like this:
A uniform plate of height H = 1.39 m is cut in the form of a parabolic section. The lower boundary of the plate is defined by: y = 0.25 x2. The plate has a mass of 4.67 kg. Find the moment of inertia of the plate (in kgm2) about the y-axis.

I know I=int(r^2)dm, but I don't know really how to apply it to this problem.
I need some help getting started, or even some info on calculating moments of inertia of random objects. Thank you.

The easiest way to approach these problems is to define the dm using all the mass that is the same distance from the axis of rotation. In this problem, the mass that is a given distance from the y-axis is all the mass that has the same x coordinate. For a plate, you have a uniform area mass density, s in kg/m^2, so a good dm would be a long thin slice parallel to the y-axis having area dA = h(x)dx where h(x) is the height of the slice at x. You can figure out h(x) from the given information and then integrate from the minimum x to the maximum x of the plate.