Rotational Dynamics

goals
Three identical blocks of length L are stacked together as shown. The blocks 2 and 3 are slided towards the right.
Figure shows a smooth fixed track with two straight parts connected by a semicircular arc $ABC$. The shown track is placed in a vertical plane. A small ball is given an initial speed $u$ along the track somewhere in the part $BC$ and collides with the track at $A$ during subsequent motion. Now answer the following questions
The figure shows an isosceles triangular plate of mass M and base L. The angle at the apex is $90^o$. The apex lies at the origin and the base is parallel to X-axis.
A solid body rotates with angular velocity $\omega=at\hat{i}+bt^2\hat{j}$, where $a=0.50\:rad/s^2$, $b=0.060\:rad/s^3$, and $\hat{i}$ and $\hat{j}$ are the unit vectors of the x and y axes.
A light thread with a body of mass $m$ tied to its end is wound on a uniform solid cylinder of mass $M$ and radius $R$ (figure shown above). At a moment $t=0$ the system is set in motion.