The Most Mind-Blowing Aspect of Circular Motion

In a way, this is a trick question. I think most people just think of the string being released from the center as being essentially the same problem as the ball detaching from the end of the string. If the problem were the latter, the ball detaching from the string, the answer would indeed be "b." The reason it's "a" is because no string is an infinitely rigid body, thus of course it would take a non-instantaneous amount of time (I imagine no faster than the speed of sound in the material the string is made of) for the ball to experience a change in centripetal force coming from the other end of the string. A question arises, what's the maximum angle that the ball can continue to subtend after the string is released? I'm guessing it's equal to the length of the string in the ideal case (that is to say 1 radian) but have no idea what it would be with the best real world material.

The moral for physics teachers is “don’t forget to specify a massless string”😁

There are a lot of comments complaining about the question being misleading, but I feel like those people are way too concerned about being right and how that affects their own egos. In reality, the video isn't about if you already know the answer, it's about learning something new, or thinking about things in a new way, and it does a fantastic job of it. It's very well communicated, a very solid length for this topic, and has a very good mix of theoretical and experimental sections. Great job and I'm looking forward to more videos!

and this is why all those Applied Math questions always stated " a non-elastic string" where they would assume the reaction to be instantaneous.

Actually the straight trajectory tangent to the circular one is NOT an approssimation. Just as you showed with the movement of a falling slinky, you should only base your calculations on the center of mass of the system. In all of the real examples the center of mass left the circular trajectory in a straight line. If you were only considering the trajectory of the ball, you should release it without the string attached. This way the position of the center of mass will coincide with the geometric center of the sphere, therefore leading to the expected result of the ball continuing in a straight line.

This is why is in all physics exams I took the questions started with "Assume you have a system with friction-less couplings in a vacuum and a perfectly uniform spherical object connected by a rigid rod to an infinitesimally small single point" because once you have to take account of material tension, air resistance and even object widths then the question gets increasing more problematic to answer correctly.

A good summary would be to say that releasing the string <> releasing the ball. The ball isn't released until the tension wave reaches it and therefore continues its circular motion.

Interesting perspective - I once did an experiment similar to this but I used a 9" nail with feathers on it like an arrow and spun it at high speed by hand at about ten feet of line. I had set up a knife so that when I wanted to "Release" the nail, I would drop down a little at the knees and let the string be cut by the knife near the nail - worked great and it really was traveling at high velocity and I believe that the tiny speck of fishing line left beyond the knife was so minuscule that it had very nearly ZERO effect on the "STRAIGHT" trajectory of the nail - Your ball that continues on the circular path is interesting looking but, in effect, is simply NOT yet truly released from the force holding in in the circular pattern. The sliding puck was a similar case because - although the puck lost enough friction to slide; it was still, partially, being restricted by friction.

As others have said. These kinds of questions assume idealised scenarios. Almost like the string vanishes from existence (like the sun in the final example). So B is the 'correct' answer. Great expansion of the concept. The falling slinky alone is a great challenge to the assumptions! Love this video

Excellent video. It boils down to definition. When released from the centre, then you're no longer talking about a ball because the object is a [ball + string]. You'd have to release the ball at the radial end of the string to remove the string from the object, and then you will get answer B. It would have been good if you replaced the string with a metal rod with a release mechanism at the end to show the trajectory of the ball on its own.

Sorry, but this video is a bit misleading. He considers the elastic property of the string but not the mass. I like that he identifies the center of mass. He mentions that it is air friction that causes the slinky or ball not to be perpendicular to the tangent of the circular path the ball travels at the ball. I assure you that it is not the only (and probably not the most) cause for that phenomenon.

Its always nice to know an event as catastrophic as the sun disappearing could take place and I would remain blissfully unaware of it.

Since we're not ignoring small details, the ball also has to rotate. We can explain it either as to conserve angular momentum since it will no longer be rotating, or because points in the ball have different speeds since they are at different distances from the center of the rotation.

Thank you. I'm a retiree with a PhD in physics. You gave me something new to think about. I had a teacher when I was a student, Prof Brian Pippard (https://en.wikipedia.org/wiki/Brian_Pippard), who loved to demonstrate simple physical systems that gave unexpected results, such as spinning potatoes. Or how to use a glass of milk, a laser and a pencil to measure the astigmatism in your eye. I class this video as being in that mold.

Very nice!. As others have said it shows the importance of those words and phrases used to make elementary problems tractable: '...light, inelastic string...', '...a point mass...`, '...a rigid rod...`, `...rolls without slipping...` or whatever. Good to see videos like this that show how removing these kinds of assumptions has measurable and often surprising effects.

Wave propagation is a fascinating thing, and is involved in surprising processes. It appears that it is involved in the swinging of a ball on a string (or slinky) in a circle...at least upon release. If you looked carefully, you could actually see a small reflected wave traveling back up the string when the tension wave reached the ball. The impedance of the ball is quite high compared to the string, resulting in the reflected wave. Same thing happens with sound waves, radio waves, and even water waves. Fascinating stuff.

I always cut my "massless" string at the ball. While I think your presentation of the question is disingenuous, I do love the video and how it sheds "light" on the finer details. Don't forget the mass (or more appropriately, the moment of inertia) of the string, this will have a similar effect without retardation (change your slinky to a solid rod). I stand by the answer "b", but admittedly to the question of motion after breaking/cutting the string at the ball. What I really like about this video is that it make one think about the real life impacts of the fictitious assumptions/simplifications we employ and quickly forget about.

Good presentation and the slow motion video with the slinky spinning the ball to illustrate the effect of finite time required to propagate the information was very impressive. I was thinking of the "what if the sun disappears" case as an example but you mentioned it at the end. That being said, the question in the beginning was tricky in the sense that most people would assume you are using "fully rigid" spring. Could have started off by clearly stating that the string is elastic, or by not even posing this question but just saying that this video demonstrates the effect of elasticity or finite speed of propagation of information on circular motion. That alone in itself is incredible in itself, as you have demonstrated in the rest of the video. This tricky question at the beginning made it hard to take you seriously in the beginning, especially when it was immediately followed by the example of an object on a rotating turntable wherein the cause of the centripetal force is frictional force and the behavior you showed (it slipping and it following a curved path) was for a phenomenon not directly related to this topic, which you didn't even get into in the video! Could have avoided the sensationalism, just my opinion.

Got me with that one. When the connection between the ball and the string is released, the correct answer is (b)... But the experiments were great anyway!

Man, just blown my mind. I didn't know that from my college. Also graphic quality as well as briefing is Extremely good. Keep up the good work