Consider the tetherball shown:
At t=0, the ball, of mass m, is moving in a horizontal circle with velocity Vo and has length Lo. The cord is now slowly drawn in until it has length Lo/3.
Vo = 20 m/sec.
Lo = 1.5 m
m = 2 kg.
What is the final velocity of the ball, and what angle does the cord make with the verticle?
This is a conservation of angular momentum problem... so IiWi = IfWf...
I am treating the tetherball as a single particle so therefore its moment of inertia = mr^2.
2((LoSin(Ø)^2))Wi = 2((LfSin(Ø+∆Ø)^2))Wf
R is given at all times by LxSin(Ø+∆Ø)... for our purposes where Lx is either Lo or Lo/3. Of course at Lo, ∆Ø=0.
Also, Tangential velocity = rw...
V = r dØ/dT
The Attempt at a Solution
So, I have been working this problem for so long that I am starting to go a bit crazy, and seem to find myself sputtering around in a rut!
It is clear to me that I have been looking at this problem a bit poorly...
I am trying to set Vdt/r = dØ and integrating both sides... but I'm not sure that is a valid operation due to the sinØ inside the radius. If it is a valid operation, then theta = 20 do after completing the IVP... But from there, how do I find the final time?
I am completely lost on this one... I think.
ANY help would be vastly appreciated.
You don't want to see the pages of failed attempts... this is about where I am right now.