# Required conditions for vertical circular motion to occur?

• I
For the case of a particle attached to an inextensible string which is hanging at rest and then provided an impulse horizontally, what conditions must the system meet in order to allow for COMPLETE circular motion. Im well aware the tension at the apex of the motion must be satisfy one of the following:
• T>0
• T≥0
So which one is it?

## Answers and Replies

berkeman
Mentor
For the case of a particle attached to an inextensible string which is hanging at rest and then provided an impulse horizontally, what conditions must the system meet in order to allow for COMPLETE circular motion. Im well aware the tension at the apex of the motion must be satisfy one of the following:
• T>0
• T≥0
So which one is it?
Welcome to the PF.

Which do you think is correct, and why? Is this for schoolwork?

Well if I'm to follow the general principle that the string must be taut at all times, it seems logical that it must be T>0. However i still think it possible for the tension to be 0 at the apex and for it to still continue perform vertical circles by gaining enough velocity to become immediately taught after it has turned an angle of ∂θ from the vertical.
This isn't for school work, I'm just curious.

Last edited:
phinds
Science Advisor
Gold Member
First, the word you are intending to use is "taut", not "taught" (unless you intend to teach the string something )

Personally, I think your analysis is correct, but it would not astonish me to find that we are both wrong for some reason.

berkeman
Is T>0, a more generalised assumption?

Last edited:
phinds
Science Advisor
Gold Member
Is T>0, a more generalised assumption?
No, it's either right or overkill. If T>=0 is sufficient there is no need to say that T>0 is required because that would imply that T=0 is insufficient.

How can we prove this?