if the velocity is seen as its path velocity, then the speed did not change. I understand that work is the change in Kinetic Energy, and that Ke is defined only by the speed variant of Velocity, not the direction. but doesn't changing direction require work to be done, or in our case, where you spin the ball on a string, the velocity is changing as direction only, but if you change the reference frame to that of an outside observer who is seeing you swing that ball around in your glass windowed truck, the speed is changing relative to them.
OK i get it. the kinetic energy is not changing relative to the pole it is fixed to, but relative to any other independent observer the KE is changing.
I recall some time ago that someone pointed out that after one revolution there is no change in position so no work was done. and it makes sense that a if work was done how come neither of the variables have change in the formula ke=1/2MV^2 it has the same mass the same speed and direction. so there could not have been any work done. (I am at home now and i was when i last posted, so i guess i have not done any work in the meantime )
So here was my assumption, I chose this assumption to help me sleep at night, there was work done, and it can be seen especially after each half rotation. but each conceutive half rotation will be work done in the opposit way so it will come back to zero.
And now I have thought about it some more, I am back to your camp, with the ball on a string or even any two points of a rotating body, if there was work done and the energy was always present but nulling it self after each half rotation, where did it come from? (My previous example was given to me years ago as a satellite in orbit, i mistook gravity as energy or a force, but now i see it as something else not too much unlike the bonding of all molecules in our spinning body. for a lack of a better work i would call it a force)
five min later I come back to make another post, it gets added to the last one I noticed..
Second post is as follows;
Oh mann I think I am having another cerebral flatulence moment.
I think I can say yes there was work done, and point to where the energy came from. in the case of the satellite and the earth, the energy was traded between each other as speed and height change relative to their CoM. a form of ke pe change. same with the stick. the stick bent and stored potential energy or if it's in your hand you were providing energy or if you were in a car the cars speed changed..... but, if it were two balls of equal mass rotating around each other then they would have no speed change relative to CoM and no height change hmmm. oops fell into a hole just then. BrB
Back again, changed CoG to CoM.
OK now i am just now realizing they (The earth and satelite) don't change distance/height position relative to their CoM, they rotate uniformly around it. hmmmmmm.. Back in a day or more.
Edited by Bryce, 24 November 2016 - 07:08 AM.