The Turntable Paradox

I can't believe I didn't make a "how the turntables" joke. That's why I love the comments section! Here's a paper with the calculations: m2.askthephysicist.com/Weltner.pdf Note that equations 18 and 19 should have R² terms. That threw me off for longer than I care to admit!

I'm gonna need a 2-dimensional, transparent, liquid filled representation of this.

'discs behave wiredly on turntables'... that sums up my entire experience of the 90's quite nicely

Well well well, how the turntables....

This is the first time in a long time that I've genuinely felt fascinated by the application of mathematics as hard-and-fast rules for how our world works. Thank you for this fascinating journey.

Would be cool to mount the top-down camera to the turntable so it rotates with it. When you mentioned the non-inertial reference frame stuff I was hoping to see the ball’s path from that reference frame.

I can't be the only one that initially thought it was pi rotations rather than 7/2 when you counted them

Seeing you advertise "The Länd" took me by surprise. I didn't know we were advertising internationally. Also, your pronounciation of "Baden Wörttembörg" is really adorable. 😄

As a physicist, this video is pure joy. Thanks for making this video available, Steve ❤️

as soon as you brought up a hollow ball and I saw the numbers 5 and 7 pop up, I thought of Moment of Inertia. I am pretty proud of my tiny noggin for thinking of that

Love the video! Wanted to say, I did my master's thesis on how students conceptualize the Coriolis force, and I'd recommend avoiding terms like "fictitious" when describing it. It gives students the impression that it's 'made up' or 'doesn't exist', which conflicts with their bodily perceptions which have experienced the force first-hand. Also, it makes it sound like it shouldn't be trusted (let alone, used), rather than emphasizing how helpful (and necessary) the Coriolis force is when viewing things from a non-inertial frame. Personally, I try to call it an "apparent" force, because it 'appears' when you change your perspective to the non-inertial frame. It's all about clarifying the contexts in which the Coriolis force is productive.

I saw this at the Experimentarium, a Science Museum in Denmark. One interesting variation is a large hollow ring (a thick bracelet or similar). If you put it on the turntable vertically and let it get up to speed, and then place a ball inside the ring, the ball inside will stabilize the motion of the ring, and behave quite similarly to a single ball.

Would have loved to see a view locked to the turntable's rotation (i.e. a camera from above rotating at the same speed, or each frame rotated to keep the turntable apparently in a fixed position). Bet the ball movement would look pretty interesting.

Your videos are simply awesome

This helps me visualize how a Lagrangian orbit can be somewhat stable despite all the forces being apparently unblanced.

The hollow ball discrepancy blew my mind. And the seeing the mathematical proof was so satisfying. I love when maths describes real world phenomenon so comprehensively.

I like that you showed some of the math here as well. I think too many youtube science channels forget that besides just describing observations we also already have a lot of very good models that can predict the observations very well.

Most of us would, I think, be surprised to see a ball on a turning turntable basically staying in one spot. Instead of explaining with formulas only, you described how it happens very simply. Great work!

A ball rolling from a flat surface, onto a turntable, back onto a flat surface, is also interesting. It swerves on the table, but exits perfectly in line with the direction it entered from.

Very good at cutting out the technicality and still keeping the explanation satisfactory