1. Can both (linear)momentum and angular momentum be simultaneously conserved?
2. What are the conditions for the conservation of momentum?

• What are the conditions for the conservation of angular momentum?
• You are given two objects, a hoop having a moment of inertia about its center of $I_{hoop}=M_{hoop}r^2$ and a long thin rod having a moment of inertia about its center of $I_{rod}=\frac{M_{rod}}{12}L^2$. The length of the rod, L = 2r. They are fused such that the rod passes through the center of the hoop and their centers of mass are in the same location and in the same plane(depicted below). What is the moment of inertia of the composite object about an axis passing through their common center of mass and perpendicular to the plane of the hoop?

Your success at the Thunderdome command center has led to your being raised to the rank of subcommander in the Scorched Earth Army. You have been sent to a remote outpost in Icy Cape, Alaska. The outpost is the first line of defense against boar tigers for the rest of humanity. It is located at the shore of a large frozen lake across from which is the boar tiger breeding ground. The outpost was formerly a foundry for metal working; several large rectangular blocks (5 $\mathrm{m}$ wide; 1 $\mathrm{m}$ high; 1 $\mathrm{m}$ deep) of steel rest on the frozen lake. The blocks are not solid, but have a wall thickness of 10 $\mathrm{cm}$. The steel made at this foundry has a density of 7850 $\mathrm{kg/m^3}$.

Roving in packs of precisely 101, boar tiger hide cannot be penetrated by conventional weaponry (i.e., bullets and knives). During the last winter, the high commander of the outpost, Dr. Hodge, commissioned the deployment of cannons to defend the outpost. The cannons were engineered to fire .3 $\mathrm{m}$ diameter cannonballs at a speed of 1600 $\mathrm{m/s}$. These cannonballs are made of clay with a very thin steel shell ($m = 200 kg$). These were found to be ineffective against the packs of boar tigers resulting in many casualties. However, in that attack, Dr. Hodge observed that boar tigers were afraid of objects with swinging or sweeping motions.

Dr. Hodge has asked you to design a defense system that can defend against packs of boar tigers using the cannons (already in place) and the large, rectangular steel blocks. In his mind, it could be possible to have the steel blocks slide and rotate along the ice, sweeping up the attacking boar tigers along the way.

To determine if such a defense mechanism is feasible, Dr. Hodge requires that you determine how the steel block will move and with what speed it could be expected to strike boar tigers.

• Was the kinetic energy of your system conserved? Why or why not? What type of collision was this?
• Was linear momentum of your system conserved? Why or why not?
• Was angular momentum of your system conserved? Why or why not?
• Sketch the motion of the end of the block.
• How does the speed of each point on the block due to rotation compare to that of its nearest neighbors?
• How does the speed of the center of mass and the speed of the end of the block depend on where you shoot the cannon ball at the block? What would happen if you shoot the cannon ball at the center of the block?
• What did you assume about the axis of rotation of the block-ball system after the collision? What could you do to make this more realistic? Qualitatively, how would this change your approach and your results?