I would like to ask a question in regards to an object's translational and rotational kinetic energy.
Up till now, my understanding was that whenever you have a rotating body, you must consider both translational and rotational kinetic energy. However, after solving a couple of problems, it has come to my attention that there are situations where you only have to consider rotational kinetic energy without having any translational kinetic energy.
For example, here is a question that I got stuck on:
"Tarzan has foolishly gotten himself into another scrape with the animals and must be rescued once again by Jane. The 60.0-kg Jane starts from rest at a height of 5.00 m in the trees and swings down to the ground using a thin, but very rigid, 30.0-kg vine 8.00 m long. She arrives just in time to snatch the 72.0-kg Tarzan from the jaws of an angry hippopotamus. What is Jane’s (and the vine’s) angular speed? " (the answer to this question is 1.28 rad/s)
Upon solving this problem, I first thought that you have to account for both translational and rotational kinetic energy for the rod and Jane, but the solutions show that you only have to take into account the rotational kinetic energy for both objects. We can see that the center of mass of the rod is clearly moving so I don't understand why that is the case?
How do we exactly know when to consider both translational and rotational kinetic energy or just one of them? How does this situation in the problem that I have given differ from that of a sphere that is rolling without slipping (in the latter, we need to consider both translational and rotational kinetic energy)?
Any kind of help you could give me would be greatly appreciated! (I am sorry if my English sounds strange - English is not my native language.)
Edit: I've added an image to show where I am struggling at. I don't understand why we don't include 1/2mJv1^2 and 1/2mVv1^2 when solving this particular question, even though we need them when we are dealing with a problem that involves, say, a ball that is rolling without slipping down a hill.