(Solved): Here is a device that can rotate freely with little friction with the axle. The radius is 0.5m, a ...

Here is a device that can rotate freely with little friction with the axle. The radius is $0.5\mathrm{m}$, and each of the eight balls has a mass of 0.3 $\mathrm{kg}$. The device is initially not rotating. A piece of clay falls and sticks to one of the balls as shown in the figure. The mass of the clay is $0.063\mathrm{kg}$ and its speed just before the collision is $11\mathrm{m}/\mathrm{s}$. (a) Which of the following statements are true, for angular momentum relative to the the axle of the wheel? The angular momentum of the wheel is the same before and after the collision. The angular momentum of the falling clay is zero because the clay is moving in a straight line. The angular momentum of the wheel + clay after the collision is equal to the initial angular momentum of the clay. Just before the collision the angular momentum of the wheel is 0 . Just before the collision $r_{?}=0.5/\sqrt{2}=0.5?\cos \left(45^{?}\right)$ (for the clay). The angular momentum of the wheel is the sum of the angular momenta of all eight balls. (b) Just after the collision, what is the speed of one of the balls? $?{\vec{v}}_f?=1\mathrm{m}/\mathrm{s}$