What happened to the energy of the Star?
The problem I am having issue with is a what if question: if the sun exploded and all that was left was a neutron star of 10 km, what would be the rotation rate be (I = .059MR^2)? So I understand the necessary math for conservation of angular momentum and energy. However, I noticed that the kinetic energy increased for the neutron star. My question is the following:
If the universe does not violate conservation of energy in these situations then why does it seem that way here? Did the energy come from the explosion? if not, then where is it coming from?
Answer
While the kinetic energy does increase, conservation of energy is not violated even if it may not be immediately obvious as to why. A more relatable situation might be a student spinning in a desk chair. If they begin with their arms and legs outstretched and then bring them in, their angular velocity will increase. Just like the star this will also increase their kinetic energy even though there does not seem to be a place this energy comes from. The reason why this occurs is because the student expends energy to bring in their arms and legs, thus doing work on the system. The hidden source of energy for the star will likely not be the explosion, as this would make the system lose energy and would have little angular effect. Rather, it is a decrease in gravitational energy. When the star becomes a neutron star, it packs much more mass into a smaller space, this means the mass that was further out had to "fall" towards the center in the transition to a neutron star. This "falling" led to an increase in kinetic energy, specifically rotational kinetic energy.
Customer support service by UserEcho
While the kinetic energy does increase, conservation of energy is not violated even if it may not be immediately obvious as to why. A more relatable situation might be a student spinning in a desk chair. If they begin with their arms and legs outstretched and then bring them in, their angular velocity will increase. Just like the star this will also increase their kinetic energy even though there does not seem to be a place this energy comes from. The reason why this occurs is because the student expends energy to bring in their arms and legs, thus doing work on the system. The hidden source of energy for the star will likely not be the explosion, as this would make the system lose energy and would have little angular effect. Rather, it is a decrease in gravitational energy. When the star becomes a neutron star, it packs much more mass into a smaller space, this means the mass that was further out had to "fall" towards the center in the transition to a neutron star. This "falling" led to an increase in kinetic energy, specifically rotational kinetic energy.