Why are s orbitals more “penetrating” than p orbitals?
I found an old slide from when I was teaching.
These are plots of the 2s and 2p orbitals for hydrogen (assuming 1 electron). The radial wave function is on the left and the probability density as a function of distance from the nucleus is on the right ($4\pi r^{2}R(r)dr$ if you understand the calculus).
You can see that there's a blob of density that comes closer to the nucleus for the s orbital. There's your penetration.