Question

Assuming R is right isocele triangle, I have to find the polar moment of inertia about its right-angle vertex, how is this thing turning? (Ref. Supplementary problems PS7 ex 3c-1)

Answer 1

Came across this definition on Wikipedia; hope this helps:
If a mechanical system is constrained to move parallel to a fixed plane, then the rotation of a body in the system occurs around an axis k perpendicular to this plane. In this case, the moment of inertia of the mass in this system is a scalar known as the polar moment of inertia.
Imagine the triangle turning in the xy-plane, with the right angle vertex as the pivot.

Answer 2

Poojat is correct. Think of it as spinning while the right-angle vertex is pinned. CW or CCW spin makes no difference.