Confused about radial/transverse and normal/tangential

[theBEAST]

Homework Statement

Here is the problem with half the solution:
http://dl.dropbox.com/u/64325990/HW%20Pictures/Capture.PNG

What I don't understand is why the speed = 30ft/s is in the transverse direction (v_θ). Shouldn't the speed of the car be in the tangential direction (v_t)?

 

[Dick]

If it's initially moving in a circular path the transverse and the tangential direction are the same.

 

[theBEAST]

If it's initially moving in a circular path the transverse and the tangential direction are the same.

Oh I see... I am just confused because looking at the path, it does not look circular. Let's say the question did not tell us that the car moves on a "horizontal circular path", instead it just says the car is moving on a "path as shown on the diagram". Then can you assume by looking at this picture it is circular? Could we still do the question?

 

[Dick]

Oh I see... I am just confused because looking at the path, it does not look circular. Let's say the question did not tell us that the car moves on a "horizontal circular path", instead it just says the car is moving on a "path as shown on the diagram". Then can you assume by looking at this picture it is circular? Could we still do the question?

I could GUESS it's approximately circular by looking at the diagram. But no, I wouldn't be able to say anything very exact. I wouldn't phrase a question like that.

 

[Sefrez]

I just seems that in the context of the problem, that it is assumed the motion is initially circular. If it was not however, giving the circular speed should still be enough. At any given instant, the tangential component is the same as the circular component at the given point. In other words it can be assumed to "stop making a circle" at any time because at a particular instant, it does't really matter what you assume. (imagine in the problem instead of being given r, you were given r - x < r, it wouldn't suggest you need assume before it was a circle or not)