# Circular Motion of a heavy object

1. Jan 31, 2006

### KD

A heavy object is attached to a spring and then it is twirled in a horizontal ciricle. Why does/does not the string stretch and discuss in terms of force that maintains circular motion.
My answer is that the string will stretch because in the horizontal circle motion, the acceleration will become less and less until it becomes constant, or zero. In order for the accleration to become less the radius has to increase, so the string will stretch.
However, this doesn't really discuss it in terms of circular motion, more centripetal acceleration. Help please.

2. Jan 31, 2006

### mathmike

the force that maintains circular motion is pointed toward the center of the circle is it not? what type of force is this? is it normal or tangential?

3. Jan 31, 2006

### DaMastaofFisix

Hmm, don't see exactly see where your logic is going. Lemme see If I can point you in the right direction.

For this case, in order for the mass to maintain its UNIFORM circular motion, there has to be a net force that points to the center of the circle. The magnitude of this force is given by mv^2/R, where m is the mass of the object, v is the TANGENTIAL velocity of the object and R is the radius of the circle. In such a phenomenon, the centripetal acceleration is constant, given by v^2/R, a non-cero constant. The tangential accelleariton however, is definately zero since the velocity is constant.

AHA, I just saw something? was your question asking about a SPRING or a string? Cause it seems that the whole stretching bit has to do with spring forces and Newotns third law. Try reading up on simple springs and the forces of uniform circular motion and try to figure out why the spring would increase or decrease it's length depending on the resulting centripetal force....Seriously...its a good brain racker.

4. Feb 1, 2006

### vaishakh

Well, A mass is attached to a spring and we start rotating it. We have to find whether the spring extends or not. Is this easy to be solved in Inerial or Rotating frame. The fact would be clear in a little while.
Inertial frame - The body is rotating. So it has to apply force toward the centre and hence the spring should compress? Is this correct? What is wrong in it? The body never applies force towards the centre. Then how is it in circular motion? Well, if you have such doubts then we can start from a little bit more clearer explanation. Let us take the body to be a certian point at a particular instant. At that instant the body has a velocity toward the tangential direction the the circular path at which it is moving. If there had been no spring it would have moven linearly from there. However it is the spring that holds the body in the circular path. So it has to apply a force toward the centre.
Rotating frame - The body is moving in a circular motion. So if we take it in the rotating frame, then there is a Pseudo Force. This Pseudo force acting on the spring due to the object directly answerss your qusetion.

5. Feb 1, 2006

### KD

First of all, thanks for your responses. And yes, I did mean SPRING, I accidentally typed string the rest of the times. Okay, let me see if I at least kind of got this.
Basically the object moves in circular motion because the spring is the force on the object towards the center of the circular path. There are conflicting forces between this force and the object's inertia. Well, I shouldn't say 'forces' because inertia isn't a force...anyway, at any given time the object "wants" to move in its straight line tangent to the circle, but because the spring is there, it can't. So the spring stretches out because of the object's tangential speed and inertia? The spring stretches as sort of a compromise between the centripetal force and the desire of the object to move tangentially?
And is this Pseudo force the centrigugal force?

6. Feb 1, 2006

### Staff: Mentor

Forget about pseudo forces (unless you've covered non-inertial reference frames). All you need realize is that for the object to go in a circle, there must be a centripetal force. What exerts that centripetal force? (And the only way for a spring to exert such a force is for it to stretch.)

7. Feb 1, 2006

### KD

OK, I feel like the answer is right there, but I'm still not getting it. Why is the centripetal force only applied when it is stretched? Just because it is restraining the object?

8. Feb 1, 2006

### Staff: Mentor

An unstretched spring will not exert a force. The more it stretches, the harder it pulls back. (See Hooke's law.)