$(28\%)$ Problem $2$: Gasang is a traditional Malaysian spinning tops game in which two or more players compete to strike each other's top out of a circle or to make the opponent's top fall over and stop spinning. The tops are custom$-$made so each one is different.

The diagram shows the view from above as two Gasang tops collide. Top A has mass $M_o$ and moment of inertia $I_o.$ Just before colliding this top has angular speed ${}_o,$ speed $v_o,$ and is moving at the angle $$ as shown. Top B has mass $0\mathrm{.}9M_o$ and moment of inertia $1\mathrm{.}2I_o,$ it has angular speed $1\mathrm{.}1{}_o$ and speed $1\mathrm{.}3v_o$ inthe direction shown just before the collision.

Just after the collision, top A is still spinning clockwise but with angular speed $0\mathrm{.}4{}_o$ and is moving entirely in the $+y$ direction with speed $0\mathrm{.}6v_o.$

$20\%$ Part $($a$)$ Why are bottoms of spinning tops $($where they touch the ground$)$ always narrow?

The small radius at the bottom means that the frictional torque will be small even if the frictional force is not.

$$ Correct!

$20\%$ Part $($b$)$ Taking counterclockwise as positive, what is the angular velocity of top B after the collision?