Hubble's law is actually related to the expansion of the universe and the relationship between the recessional velocity of galaxies and their distance from us. It does not directly explain why galaxies spin faster as you move out from the center. However, I can provide information on why galaxies exhibit this behavior, which is known as galactic rotation curves, and the role of dark matter in it.
Galactic rotation curves describe the distribution of rotational velocities of stars or gas clouds within a galaxy as a function of their distance from the galactic center. According to the laws of classical mechanics, objects farther from the center should have slower velocities. However, observations have shown that the outer regions of many galaxies, including spiral galaxies, do not follow this expected pattern. Instead, they exhibit a "flat" rotation curve, where the rotational velocity remains roughly constant or even increases with increasing distance from the center.
The explanation for these flat rotation curves lies in the distribution of mass within galaxies. Visible matter, such as stars and gas clouds, cannot account for the observed rotational velocities. If galaxies contained only the visible matter, their outer regions would not have enough mass to explain the observed velocities. This discrepancy between the predicted and observed mass distribution led to the proposal of dark matter.
Dark matter is a hypothetical form of matter that does not interact with light or electromagnetic radiation, making it invisible to our telescopes. It does not emit, absorb, or reflect electromagnetic radiation, hence the name "dark." The presence of dark matter in galaxies can explain the observed flat rotation curves.
Dark matter is thought to pervade galaxies and form a "halo" around them. The additional mass of the dark matter halo, combined with the visible matter, generates a gravitational force that extends farther from the galactic center and keeps stars and gas clouds in the outer regions moving at higher velocities than expected. This gravitational effect from dark matter provides the extra "pull" necessary to maintain the observed rotational velocities.
The exact nature of dark matter is still unknown, and it remains a subject of ongoing research and investigation. Various theories propose different particles or exotic forms of matter that could make up dark matter, but so far, direct detection has not been successful. However, its gravitational effects on galaxies, including the flat rotation curves, are well-supported by observations.
In summary, the faster rotation of galaxies as you move out from the center can be explained by the presence of dark matter, which provides additional gravitational influence and helps to account for the observed velocities of stars and gas clouds in the outer regions.