# Required conditions for vertical circular motion to occur?

• whit3r0se-
In summary, if the string is taut at all times, then it must be T>0. If the string is not taut at all times, then it can still perform vertical circles by gaining enough velocity to become immediately taught after it has turned an angle of ∂θ from the vertical.

#### whit3r0se-

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. I am 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?

whit3r0se- said:
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. I am 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.

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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?

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whit3r0se- said:
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?

## 1. What is vertical circular motion?

Vertical circular motion is a type of motion in which an object moves in a circular path that is perpendicular to the ground. This means that the object is constantly changing direction and velocity as it moves around the circle.

## 2. What are the required conditions for vertical circular motion to occur?

The two main conditions for vertical circular motion to occur are a constant force acting towards the center of the circle (centripetal force) and a sufficient speed to maintain the circular motion. In addition, there must be a curved path or track for the object to follow.

## 3. How is centripetal force related to vertical circular motion?

Centripetal force is the force that keeps an object moving in a circular path. In the case of vertical circular motion, centripetal force is responsible for pulling the object towards the center of the circle and preventing it from flying off in a straight line.

## 4. Can vertical circular motion occur without a centripetal force?

No, vertical circular motion cannot occur without a centripetal force. This force is necessary to maintain the circular path and prevent the object from moving in a straight line.

## 5. What factors affect the speed and radius of vertical circular motion?

The speed and radius of vertical circular motion are affected by the mass of the object, the amount of centripetal force, and the shape of the circular path. A heavier object will require more force to maintain the circular motion and a smaller radius will result in a higher speed.