This is my favorite! Love your reaction

YOU SHOULD MAKE A VIDEO MAN! I think you are absolutely correct!

Yes it did, you are absolutely correct. Yes it also took that energy from the height of the block. But it was such a small amount that it showed no difference. The upward movement took enormous force in comparison because it had to fight gravity. the spinning had very little in it's way to keep spinning or to start spinning (bit of: inertia, air friction).

Good point. The block is essentially rotating on frictionless bearings, so getting it spinning will be an almost lossless transfer of energy.

Here is the deal, angular acceleration happened around the center of gravity of the block system. This means that the NET torque had to be concentric with the center of mass of the system. Because there are two possible "torques", you need to sum them up to equal the net torque. Because the net torque is concentric with the center of mass, so will the other two torques. Because the force of gravity is applied at the center of mass and is also concentric with it, that means it's R must be 0.

I agree with your conclusion. It's the conservation of momentum: momentum_initial == momentum_final, so the separate momentum of the forward motion of the bullet and the static block MUST be conserved both while the block and bullet are separate, and after they collide.

The spinning is caused by the moment of force created by applying force that is not in line with the spinning axis (in this case the center of gravity). This creates a force pointing to the axis causing the spin. It's the same principle when you try to lift something with a lever, to lift something heavy with a low force you need a longer beam.

And I believe the energy used to make the block spin came from a slight difference in depth the bullet penetration. The non-spinning block simply absorbed more kinetic energy from the block as friction, while the spinning block used some of that energy (that otherwise would have been friction) to start spinning.

Yes, in fact, if you carefully see the high speed, the left block was a few millimeters higher. It could be because of wind or rubbing on the plastic or not proper powder charges or a whole number of things, but I attribute it to this spinning action.

I haven't finished a college level course in physics yet (i'm taking one now!) but here is my representation of what is going on: y=spinning block, x= stationary block

This means less energy is wasted in the second collision. When the block is hit off-center, the side of the block that the bullet hits recoils faster than the rest of the block (because it starts rotating) and the bullet doesn't penetrate as far, resulting in less energy being wasted as heat.

Well thought! But still the fact that one is rotating indeed means that the energy (even though is the same amount) is happening in different ways in both experiments. The rotational energy that the second block has and the first didn't is given by the way the bullet hits them, different paths mean different velocities.

Yes, we live in a world where to get something to move and keep moving, it takes energy. It is hard to wrap the brain around the idea that motion and acceleration are two very different beasts, and that motion is a constant as long as there are no forces to stop it.

This makes sense. Think of an astronaut spinning the block on a space station. The block would keep spinning a long time even with a tiny amount of force applied.

assume that, velocity of bullet before impact was 600m/s, weight is 3g and weight of block is 450g, total energy before impact is 1/2*0.006*600^2= 540 joule,