Though this question is old and has an accepted answer, I really don't feel the apparent confusion of terms and concepts in the question has been covered. Therefor let me add a try to clear this out.
In this case, the tension of the string acts as a centrifugal force that keeps the object moving in a circle.
Not centrifugal but centripetal.
- Centrifugal force is the feeling of being pushed outwards while in a circular motion (being pushed to the side of a car that turns).
- Centripetal force is the force (the resulting force) acting to keep an object in a circular motion. To do this, it must be pointing directly towards the center, perpendicular to the motion.
if centrifugal force is the only force acting on the object, why doesn't it collapse into the center? I am pretty sure this has to do with the object's inertia
Again, assuming you mean centripetal.
As mentioned above, the centripetal force is perpendicular to the motion. What happens when you move in one direction and is pulled to the side? This pull will pull you towards the center (towards the origin of the pull), only if you are standing still. If you are moving, then the pull will make you move towards the center, but at the same time you still move straight ahead. Your net movement is therefor not towards the center, but rather around it.
When you ask the question, you are making the mistake of connecting speed $\vec v$ directly with force $\vec F$. But remember that it should rather be $\vec a$ that is connected to $\vec F$. That means, force and velocity are not going in the same direction necessarily, only force and the change of velocity. And in this case, you change the radial velocity component, but keep the tangential velocity component constant - there is only acceleration (change of velocity) in the radial direction, but the net velocity is point in another way.
Also, what keeps the string taut during the swinging?
The explanation that the string is always taught is simple: The object doesn't move towards the center. When the centripetal force (the tension in the string) tries to pull the object closer, the object actually doesn't get closer. It only changes direction.
If you pull harder, then it will gain a larger radial acceleration, but since the speed must be kept constant (as there is no tangential acceleration to change the speed), the radius will change according to
$$a_{rad}=\frac{v^2}{r}$$
and the object comes closer. But if the force is just kept constant, then there is no change of radius during the motion.
There has to be some force countering the centripetal force that keeps the string tight.
No, why should there? I think you mix up the Newton's 1st and 2nd laws. The idea that counteracting forces must be present is when we have a situation of no acceleration; Newton's 1st law $$\sum \vec F=0$$
Then to reach a sum of $0$, all forces must be balanced by other forces. But since there is acceleration, namely radial acceleration in the direction of the centripetal force, then we must use Newton's 2nd law:
$$\sum \vec F=m\vec a$$
Here there is no requirement of a counteracting force to balance any other force. We just need force to cause this acceleration. And the centripetal force is doing exactly that: causing the radial acceleration.
but can a pseudo-force balance a real force?
No. Centrifugal force (not to confuse with centripetal force) is, as you point at, not a force. Just a "feeling" that you are being pushed out of the circle. Like when you are pushed to the side of car while turning. But this feeling is not a force, it is simply the acceleration that you feel. During a turn in a car, your body wants to just continue with the present speed and direction. The car then forces your body to follow along, and you are therefore pushed inwards by the car, which gives you the feeling of being squeezed into the side of the car.
Also, if centripetal were to be balanced by the pseudo-force, wouldn't the object not move at all (since the net force would be 0)?
Remember that it is not no motion but rather no acceleration (no change of speed) that is implied when the net force is zero. The speed should not be considered at all when looking at forces, and that is a key point to realize. Newton's 2nd law that combines forces with motion, is only connecting force with acceleration not with speed.
Here is an attempt to explain what is going on in the (inertial) frame of reference of the world:
The red vector is the force from the side of the groove on the ball: as a result the ball starts to move. Initially, it will get the same lateral speed as the groove - if it's at a distance $r$, and the disk rotates at $\omega$, the velocity will be $v=r~\omega$.
A moment later, the groove will be at a different angle - but the ball tries to keep going in a straight line. It will have moved to a new radial direction, where the groove is going faster than the ball. As a result, it will once again feel a force of the wall, and it will accelerate in a new direction; I tried to indicate the new velocity as the vector sum of the old velocity plus the acceleration.
Obviously you can repeat the diagram for subsequent positions of the disk.
In the rotating frame of reference of the disk, you can describe the same thing in a different way. In a rotating frame of reference, there appear to be two fictitious forces: the centrifugal force that makes the object "want to move away from the center", and the Coriolis force that is only apparent if the object has a velocity in the rotating frame of reference.
When the ball is stationary in the groove (in the rotating frame of reference), the only force it experiences is the centrifugal force (this is right after the initial impulse that will have given the ball the same velocity as the part of the groove where it was placed). As soon as it starts moving outwards (under the influence of the centrifugal force) it will also start to swerve (under the influence of the Coriolis force). The groove will exert a force equal and opposite to the Coriolis force to keep the ball moving in a straight line in the groove.
In the rotating frame of reference, the radial acceleration of the ball can be calculated directly from the centrifugal force. The total velocity can be arrived at by calculating both the radial and tangential components of the velocity (tangential velocity is $r\omega$).
I will leave the details up to you.
Best Answer
For the block to move in a circle, there must be a centripetal force (as you have said)--something needs to be constantly pulling the block toward the center of the circle if it is to move in a circle. The thing that does the pulling in this case is the spring. (In other words, the source of the centripetal force is the spring. Without the spring, there is no centripetal force, assuming there is no friction between the block and the rod.)
If this is not clear, imagine what would happen if the spring was not attached to the block. When the rod begins to rotate, the block will soon slide off the end of the rod because we know from Newton's First Law that the block will try to move in a straight line unless we apply a force to change its direction. If the spring is attached to the block, however, when the block tries to go straight and slide off the end of the rod, the spring will stretch and apply a force toward the center of the circle. That will prevent the block from flying off the end of the rod.