The Turntable Paradox

The Turntable Paradox

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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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Here’s a paper with the calculations: Note that equations 18 and 19 should have R² terms. That threw me off for longer than I care to admit!

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45 Responses

  1. Steve Mould says:

    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: Note that equations 18 and 19 should have R² terms. That threw me off for longer than I care to admit!

  2. Weeeeems says:

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

  3. MrSkypelessons says:

    I have always found spinning things and reference frames fascinating, and as an English teacher, I find it fascinating that these very real forces are referred to as fictitious forces and pseudo forces and imaginary forces. I suppose it is to separate them from contact forces and EM forces, but it does seem odd to me. I read that even gravity is a fictitious force. If there’s one thing we can be certain of, it’s the force sticking our bodies to the floor. Very interesting video and very clearly explained. Thanks.

    • MrSkypelessons says:

      @Josh Gordon I do appreciate the answer, but try saying ‘in reality, there was NO force’ to someone who was badly injured or even killed by such a force. Surely there was such a force, and not just from his perspective – from our perspective too.

      And why have I read that gravity is also ‘a fictitious force’? Is it because relativity claims (and I certainly can’t understand the logic) that gravity is just a curvature of space and time? I have no idea!

    • Josh Gordon says:

      Fictitious forces are not real forces. They do not actually exist like any of the fundamental forces (e.g. electromagnetic or gravitational), but they are very much necessary in order for someone in a non-inertial (i.e. accelerating) reference frame to explain what they are experiencing. As an example: you are a passenger in a remote-controlled car that is moving at a constant speed in a straight line. The car has no windows and has absolutely perfect wheels, shock absorbers, etc. such that you cannot even tell you are moving. Unfortunately, you are also not wearing your seatbelt. All of a sudden, someone turns the wheels sharply to the right via remote control. You will go flying into the left side of the car. From your perspective inside of the vehicle, you have no way of knowing that someone has caused your car to turn. From your perspective, there was suddenly a violent force pulling you into the side of the vehicle. What force has caused this experience for you? In reality, there was none, however from your perspective it must have been so, and so we would attribute (from your perspective) a fictitious force called the centrifugal force. Hope this helps!

  4. Chrismofer says:

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

  5. Thomas Shaddox says:

    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.

    • Benjamin I. Smith says:

      The on the table perspective would simply be seeing the ball move from right to left, right to left, right tp left. The interesting visualization is to see the path traced out by the ball. That shape is called a hypocycloid

    • That Freedom Guy says:

      Yep and from the balls perspective too. Computer machines can grind that out.

    • MrDaraghkinch says:

      @Rae S spirograph?

    • John Smith says:

      @Madsciencestache he mentions in the video that it cuts a perfect circle in vacuum without slippage, and a spiral with slippage.

    • jetison333 says:

      its possible to just stabilize the video on the turn table, if someone wanted to put in the effort.

  6. trustnoone81 says:

    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.

    • JordanPeterson SucksMonkeyButt says:

      @pineapplepenumbra haha, thanks!

    • pineapplepenumbra says:

      @JordanPeterson SucksMonkeyButt It helps that your post was good, but I thumbed you up before I read it, just because your name deserves it.

    • JordanPeterson SucksMonkeyButt says:

      @Luke Downes Luke Downes by closed form equations they mean that the equation can be solved analytically which generally leads a nice solution. Otherwise you have to solve it numerically.

    • ᛋᛒᛖ‍ᚱᚫᛞᚻᛏ says:

      @Luke Downes Luke Downes Equations are closed, formulas are open.

    • Luke Downes Luke Downes says:

      I’m curious. What is your thoughts on open and closed formulas relative to physics?

  7. Oskari Liukku says:

    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.

  8. Blaise says:

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

  9. Jörg Reinhardt says:

    ‘discs behave wiredly on turntables’… that sums up my entire experience of the 90’s quite nicely

  10. Gregory Von Dare says:

    Sounds like a way to understand precession and LaGrange Points. There’s something deep about gravity and dynamics in this demo, but I can’t quite crystalize it. Any ideas about that, Steve?

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