Question

Find the frequency of small oscillations for a thin homogeneous equilateral triangular plate if the motion takes place in the plane of the plate and the plate is suspended from one apex.

I have this answer, but I would like to know why did he use kinetic energy as 1/2 I(theta)dot^2 instead of 1/2 mv^2 and changing it to polar coordinates to get 1/2 m(a^2+ a(theta)dot^2?

lagringian of Re the system 2 1: Kifi-pie II OPE. - since plate is supended from apex So Mommol of Inertia about axis passing through o' In 5. mq2 where a = side of equilateral 12 Contence of mass is at triangular plate from vertex -Ma dem = so PoE. = -mg / sin coso 2= 1 ) ma? q2 + mga / dy coso - Lagrangian equ of motion en om de ce co _mga pa sino u no mazaj