What is the condition for the string becoming slack in circular motion?

Answer 1

An external force greater than the force needed to make the object go in a circle. For example, if I twirl an object along a vertical plane (upright), the string will stay tight only if I twirl the object fast. When the object is moving fast, a large force is needed to make the object go in a circle, which is supplied by the string. If you let go of the string, you will be removing this force and the object will fly off in a straight line. If I let the object slow down, the object will continue to move in a circle, but with less and less force needed to force the object into a circle. Eventually, the downward force of gravity will be greater than the force on the string when the object is moving up, and the string will go slack during part of the circle. The object will move upwards and then fall down, not forming a true circle. You could do the same thing by simply hitting the object inwards while it is moving, you are supplying an external force that is greater than the force needed to make the object go in a circle.

Answer 2

I'll have to guess at your meaning. If you mean rotating something around that is tied to a fixed point by a string, the string will become slack only if another force becomes involved in addition to the centripetal force caused by the string. ("Centrifugal" force is an illusion created by the effect of inertia on the moving object).

For instance, if the string is in your hand and you jerk the string a little and then return your hand to its original position, the object will move inward in its circle of rotation, then the string will be slack for an instant until its inertial momentum returns it to its circular path.

If you place an object on a flat surface, and remove all forces other than the force of the string, the object's momentum will keep the string taut until friction slows it down and stops it. (under perfect conditions, the string will still be taut.)

Answer 3

An external force pushes the object on the end of the string towards the center with a force greater than that required for uniform centripetal motion (greater than the tension of the rope is in normal circular motion).

Answer 4

If you are talking about vertical circular motion, then the condition is T=0 i.e. when tension becomes zero.

Answer 5

Other forces (such as gravity) are greater than centripetal force.
or
Linear motion is faster than circular motion.

Answer 6

gravity becomes more than centripetal force.