The Turntable Paradox

A ball on a spinning turntable won't fly off as you might expect. In fact the ball will have it's own little orbit that is exactly 2/7th the angular speed of the table. Here's why.

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[SteveMould]

I can't believe I didn't make a "how the turntables" joke. That's why I love the comments section!

[weeeeems]

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

[WinEntity]

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.

[tshddx]

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.

[freddym]

Well well well, how the turntables....

[jaredarnell]

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.

[MyriadCelestia]

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

[carljohanr]

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.

[AlDunbar]

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!

[luizucchetto]

Your videos are simply awesome! I am a rerired Physics Teacher and could have used your videos to engage and challenge my students while I was teaching. I never miss your videos and thank you for keeping my love of Physics alive and I hope inspiring a whole new generation of young students to take up the challenge of physics and science in general.

[JoshHenderson]

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.

[chrismofer]

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

[trustnoone]

I started chuckling to myself the second I saw the equation for the moment of inertia of a ball. This was so cool! It's nice to see some interesting physics can still be done with closed form equations.

[ignispurgatorius]

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.

[Bob_Adkins]

I imagine the formula for the motion of a slightly elliptical ball would be terrifying.

[DaHoodedBandit]

I love how you can see the line bent with the rolling shutter effect when he pauses the video. So cool

[batlin]

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.

[oskioskioski]

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.

[blaise]

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