Radial Co-ordinate of a ball from the origin

[RippyTheGator]

1. A Ball is in a frictionles tube that is rotating with a constant angular velocity $\omega$. The ball is initially held in place a distance r₀ from the pivot by a string which breaks at t=0. If the radial coordinate of the ball from the origin is r(t), find r(t).

I am having a very hard to picturing this, and what the system is actually doing. I know I have to deal with polar coordinates.


jI don't really have an attempt at this solution because I do not know where to start really, I can't picture the diagram in my head. I know this isn't much to help me on, but any push in the right direction would be much much appreciated.

 

[Spinnor]

What class is this for? What are you learning that would be relevant.

 

[daveb]

From the description, it sounds as if the ball is in the tube, and the tube is rotating around one end at some pivot point. The string breaks, the tube is still rotating around the pivot. The ball is still constrained inside the tube but no longer has radial acceleration (since the string is now broken), only tangential. Of course, r(t) will change once the ball leaves the end of the tube (unless you assume it is infinitely long).

 

[Spinnor]

You wrote,

"Of course, r(t) will change once the ball leaves the end of the tube (unless you assume it is infinitely long)"

Won't r(t) change before it leaves the tube, otherwise it won't leave the tube?

 

[daveb]

Yes, I mean it will probably be a piecewise function because while it's still in the tube, it is constrained to move within the tube (which is still moving), but afterwards it is no longer constrained - haven't done the math, it may not be piecewise.

 

[RippyTheGator]

I figured it out, so no need to reply anymore. Thanks though! And Spinnor it is a Classical Mechanics course. It is a question dealing with vector components in Spherical coordinates.