A pulsar.
Studying star and star types can be fun, but it can be challenging to remember each type. A Neuron star is a dense, rapidly spinning star.
Because the star that blew it off of itself was rotating. Conservation of rotational momentum.
White dwarf
how dense the star is
Because they do. In many cases, a "why" question about a physical fact is pointless. Facts are. We can theorize, fairly safely, that the original cause of the star's rotation is that the coalescing stellar nebula had some angular momentum prior to its collapse. Since angular momentum is ALWAYS conserved, the gravitational collapse would force a widely dispersed, slowly rotating nebula to collapse into a very dense RAPIDLY rotating star.
The small dense remains of a high mass star are either a neutron star or a black hole, depending on the mass of the original star. Neutron stars are formed from the core collapse of a massive star and are incredibly dense, composed mainly of neutrons. Black holes are formed when the core collapse results in a singularity with infinite density and a gravitational pull so strong that not even light can escape.
White dwarf
The fastest rotating body in the solar system is the star, Regulus. It has an equatorial rotational velocity of about 288 km/s.
An extremely dense dying star is called a neutron star. It is formed when a massive star collapses in a supernova explosion, leaving behind a core made mostly of neutrons. Neutron stars are incredibly dense, packing the mass of the sun into a sphere only about 12 miles in diameter.
"Small but very dense" sounds like the description of a neutron star or "collapsed matter star". Theoretically, a black hole (the only thing more dense) has no physical size at all. So, "neutron star". If the neutron star is spinning rapidly, they are called "pulsars" for the radio-wave pulses that they generate.
Rotating airport beacon.
earth is rotating on its axis