You can distinguish between a raw egg and a hardboiled one by spinning each one on a table. Explain how. Also, if you stop a spinning raw egg with your fingers and release it very quickly, it will resume spinning. Why?

The raw egg contains more of the liquid in it and when you rotate it the centrifuge will act on the liquid and push it against the inner surface of egg. This increases the rotational inertia of the egg and it spins slowly. On the other hand, the hardboiled egg will have lower rotational inertia and will spins fast relative to the raw egg.
When the raw egg starts rotating, the liquid inside the egg gains angular momentum. With large rotational inertia, the liquid’s angular momentum will not be lost quickly and in time for which you stop the egg.
Therefore when you release the egg again, it will start spinning again because of the angular momentum of the liquid.

Hard boiled egg act as a rigid body, while rotating. In case of raw egg, the liquid matter try to move away from the centre,thereby increasing its moment of inertia. As moment of inertia is more, the raw egg will spin with smaller angular velocity provided, same torque is applied in both the cases. Hance hard boiled egg will spin faster.