4 ms·

I grew up on Martin Gardner in the 70's and 80's, so I'm always happy to see him referenced. My favorite physics puzzle of his is: If you heat a solid iron toru

I grew up on Martin Gardner in the 70's and 80's, so I'm always happy to see him referenced. My favorite physics puzzle of his is: If you heat a solid iron torus, does the radius of the hole in the middle grow or shrink?

itishappy 2y ago
Love that one, and the closely related hole in a large metal plate. Something about that reframing flips my intuition on it's head.
aj7 2y ago
Grow, of course. I mean, come on.
- jagged-chisel 2y ago
  Some intuition says one must consider the outer iron expanding into the hole. Some thought allows the realization that the only direction for expansion is outward.
  - wat10000 2y ago
    Or consider that, assuming the expansion is uniform, it's applying a scale transform to the object and otherwise leaving the shape exactly the same. All aspects of the shape will therefore grow larger.
    - jagged-chisel 2y ago
      This is a novel way to think about it that hadn’t occurred to me. Thanks!
zellyn 2y ago
[Edit: removed spoiler] You can gain a bit of intuition about growing and shrinking circles by imagining them to be squares with _very_ rounded corners, or equivalently, imagining what happens if you lengthen them by inserting straight lengths in four places, turning them into squares with very rounded corners. For example, the old question of: if you have a rope lying on the surface of the earth all the way around a great circle, and make it 10m longer, how high could it be above the surface? Even though the square-with-corners thing helps me visualize it quite perfectly, I _still_ find it weird that that the answer is 1.5m!
- nialv7 2y ago
  Or you could imagine an infinitely thin torus.
SamBam 2y ago
Anyone who's opened a tight jar lid by putting it under hot water should know the answer to this instinctively.
jaredhallen 2y ago
This thought experiment has at least one very useful practical application, and the timing of your comment is quite the coincidence. I'm getting ready to heat up a differential pinion bearing retainer (Ford 9" style) in a toaster oven right now...
ultimafan 2y ago
Interesting to see this presented as a puzzle- I've never thought about it academically, but knew the answer immediately from hands on experience. Slipping metal bearings over metal shafts when the inner diameter of the bearing is less than the outer diameter of the shaft is a piece of cake if you throw the bearing into a toaster oven for 15-20 minutes first. It'll drop right on right down to the base no problems. When they're unheated you wouldn't be able to get them on and down even with a significant amount of brute force hammering.

itishappy 2y ago

Love that one, and the closely related hole in a large metal plate. Something about that reframing flips my intuition on it's head.

aj7 2y ago

Grow, of course. I mean, come on.

jagged-chisel 2y ago
Some intuition says one must consider the outer iron expanding into the hole. Some thought allows the realization that the only direction for expansion is outward.
- wat10000 2y ago
  Or consider that, assuming the expansion is uniform, it's applying a scale transform to the object and otherwise leaving the shape exactly the same. All aspects of the shape will therefore grow larger.
  - jagged-chisel 2y ago
    This is a novel way to think about it that hadn’t occurred to me. Thanks!

zellyn 2y ago

[Edit: removed spoiler] You can gain a bit of intuition about growing and shrinking circles by imagining them to be squares with _very_ rounded corners, or equivalently, imagining what happens if you lengthen them by inserting straight lengths in four places, turning them into squares with very rounded corners. For example, the old question of: if you have a rope lying on the surface of the earth all the way around a great circle, and make it 10m longer, how high could it be above the surface? Even though the square-with-corners thing helps me visualize it quite perfectly, I _still_ find it weird that that the answer is 1.5m!

nialv7 2y ago
Or you could imagine an infinitely thin torus.

SamBam 2y ago

Anyone who's opened a tight jar lid by putting it under hot water should know the answer to this instinctively.

jaredhallen 2y ago

This thought experiment has at least one very useful practical application, and the timing of your comment is quite the coincidence. I'm getting ready to heat up a differential pinion bearing retainer (Ford 9" style) in a toaster oven right now...

ultimafan 2y ago

Interesting to see this presented as a puzzle- I've never thought about it academically, but knew the answer immediately from hands on experience. Slipping metal bearings over metal shafts when the inner diameter of the bearing is less than the outer diameter of the shaft is a piece of cake if you throw the bearing into a toaster oven for 15-20 minutes first. It'll drop right on right down to the base no problems. When they're unheated you wouldn't be able to get them on and down even with a significant amount of brute force hammering.