Rotational Inertia of a triangle

[rpthomps]

Homework Statement

A thin, uniform vane of mass M is in the shape of a right triangle, as shown. Find the rotational inertia about a vertical axis through its apex, as shown in the figure. Express your answer in terms of the triangle’s base width b and its mass M.

Homework Equations

The Attempt at a Solution

The answer in the back is just $b^2M/2$ without the second term.

 

[TSny]

It's not clear what is meant by "a vertical axis through the apex". Your answer looks correct if the vertical axis is perpendicular to the plane of the triangle and passes through the lower left vertex of the triangle in your drawing. The answer in the back of the text appears to be correct if the axis is in the plane of the triangle, passes through the lower left vertex, and is perpendicular to the base b.

 

[rpthomps]

Okay, thanks for looking it over.

 

[haruspex]

The word 'vane' implies to me that the axis is coplanar with the lamina.
rpthomps, your r is wrong. You want the distance from the axis, not the distance from the apex.