Problem $1(25$ pts$)$

The equilateral triangle of mass $m$ is given a slight push to the left when $=0$ and it rotates about the comer of the table at $O.$ Each side of the triangle has length $l$ and $I_G=\frac{1}{12}m{l}^2.$ Determine

$($a$)$ the angular acceleration of the triangle as a function of $g,l,$ and $,$

$($b$)$ the angular speed of the triangle as a function of $g,l,$ and $,$

$($c$)$ the normal and frictional force between the triangle and the table as a function of $m,g,$ and $.$

Extra Credit $(10$ pts $)$: If the coefficient of static friction between the triangle and the table is ${}_s=\frac{1}{2},$ determine the angle in degrees at which the triangle will start to slip on the table.