Confusion about moment of inertia

[Hoshiiiiiiiiiiiii]

When a question only asks for the moment of inertia (of say, a T-section), do I have to find the moment of inertia with respect to both the x and the y axis?

 

[haruspex]

When a question only asks for the moment of inertia (of say, a T-section), do I have to find the moment of inertia with respect to both the x and the y axis?

In the absence if any other information, it would be about an axis through the mass centre, but that still leaves open more than one possibility. If it is essentially a 2D shape I suggest an axis normal to that.
Please post the whole question, word for word, with any diagrams.

 

[Hoshiiiiiiiiiiiii]

The question says "Calculate the second moment of area of the T-section given below" with this diagram

I have found the moment of inertia with respect to both axes correctly, but I'm confused whether I should leave them like that or add them together to get the polar second moment of area.

 

[haruspex]

The question says "Calculate the second moment of area of the T-section given below" with this diagram https://www.physicsforums.com/attachments/shear-stresses-on-beam-mechanics-of-solids-41-1-jpg.234480/?temp_hash=efb03e1eeffac051d9d9072edf2482c7

I have found the moment of inertia with respect to both axes correctly, but I'm confused whether I should leave them like that or add them together to get the polar second moment of area.

The image us not working for me. Nothing happens when I click the icon.

 

[Hoshiiiiiiiiiiiii]

The image us not working for me. Nothing happens when I click the icon.

I edited my reply. I think it's working now.

 

[haruspex]

I edited my reply. I think it's working now.

Yes, I see it now.
I stick with my earlier guess: take the axis as being through the mass centre and normal to the plane.

 

[Hoshiiiiiiiiiiiii]

Thank you so much!

 

[Benjamin_harsh]

take the axis as being through the mass centre and normal to the plane.

Does it simply mean calculating MOI at centriodal axis?

 

[haruspex]

Does it simply mean calculating MOI at centriodal axis?

AS far as I am aware, a centroidal axis is any axis that passes through the centroid. See e.g. https://www.quora.com/What-is-the-difference-between-Neutral-axis-and-Centroidal-axis.
Also, please do not keep referring to an MoI "at" an axis. An axis is a line. Write MoI about an axis.

For a lamina, a centroidal axis could be within the plane of the lamina, at any angle, or not even within the plane.
A useful theorem is the perpendicular axis theorem. This says that you can find the MoIs about any two such axes at right angles in the plane and add them together to find the MoI about the axis through the centroid and normal to the plane.