Intepretation of question only

[negation]

Homework Statement

Three equal masses m are located at the vertices of an equilateral triangle of side L, connected by rods of negligible mass. Find expressions for the rotational inertia of this object (a) about an axis through the center of the triangle and perpendicular to its plane and (b) about an axis that passes through one vertex and the midpoint of the opposite side.

The Attempt at a Solution

I'm facing only issue with intepreting part(b). What does it mean for an axis that passes through one vertex and midpoint of the opposite side? How can it both be 2 place at once?

 

[SteamKing]

I'm facing only issue with intepreting part(b). What does it mean for an axis that passes through one vertex and midpoint of the opposite side? How can it both be 2 place at once?

It means the axis lies in the same plane than is formed by the three masses, not perpendicular to said plane.

 

[negation]

It means the axis lies in the same plane than is formed by the three masses, not perpendicular to said plane.

That would mean the axis cuts the vertice and the opposite length L at the midpoint. This is understandable. But isn't the question asking for the axis to be perpendicular to the plane in part(A)? For (B), isn't it asking for the axis to be perpendicular to the plane and yet cut one vertice while simultaneously cutting the midpoint of the length opposite to the vertice?
Just wondering how it's possible for the axis to be a normal to the xy plane while at the same time being superimposed on the xy plane..

 

[SteamKing]

In three dimensions, you can have up to three mutually perpendicular axes of rotation. While Part a) clearly specifies that the axis of rotation passes thru the center of the triangle and is perpendicular to the plane of the three masses, Part b) specifies the axis which passes thru one vertex AND the midpoint of the opposite side of the triangle. I know no geometry which allows both of these conditions in Part b) to be satisfied while the axis is simultaneously oriented perpendicular to the plane of the masses.

 

[negation]

In three dimensions, you can have up to three mutually perpendicular axes of rotation. While Part a) clearly specifies that the axis of rotation passes thru the center of the triangle and is perpendicular to the plane of the three masses, Part b) specifies the axis which passes thru one vertex AND the midpoint of the opposite side of the triangle. I know no geometry which allows both of these conditions in Part b) to be satisfied while the axis is simultaneously oriented perpendicular to the plane of the masses.

Going by your intepretation, I managed to solve the problem. Thanks