Their total momentum after the push is zero, just as it was before they pushed off each other.

For example, the total momentum of both particles put together would be (roughly) the same before and after they act on each other.

These relations do not give the total angular momentum of the electron.

The quantum number J refers to the total angular momentum, as before.

Because its total angular momentum remains the same during this process, the rotation rate increases.

When considered together, the object and the mass constitute a closed system in which total momentum is conserved.

This places a constraint on the change in total angular momentum.

In the example you gave, the total momentum was 1000 kg m/s.

That must be the total momentum after the collision.

You will see that total momentum and total energy are conserved.