3 ms·

Yes, but that intuition doesn't seem to work for the case where small disk is rolling around the inside of large one, not outside. What's the intuition for why

Yes, but that intuition doesn't seem to work for the case where small disk is rolling around the inside of large one, not outside. What's the intuition for why we then subtract one rotation rather than adding one ?!

HenryPrickett 3y ago
Very basically, to go the same direction, a small disk on the inside and the outside of a large disk need to spin opposite directions. When you're on the outside, your spinning direction agrees with the direction you go around the circle (i.e. the rotations add). When you're on the inside your spinning direction is the opposite of the direction you go around the circle (the rotation subtracts).
ahepp 3y ago
It’s concave rather than convex? It’s bending into itself instead of away from itself?
7734128 3y ago
You're intuitively rolling the other way. Going on the surface means that you're falling forwards while going inside means that you're falling backwards.
icegreentea2 3y ago
I think you can always arrive at the correct answer by tracking the distance traveled by the center of the rolling object. In the original SAT question, the center of the rolling circle is 4r from the center. That means it travels an arc of 8pi. Then assuming no-slip, that works out to 4 rotation. In your case, rolling on the inside, the center of the rolling circle will only be 2r from the center. Using the same logic, this yields 2 rotations.
- bearmode 3y ago
  This is definitely the easier way to understand it. Imagine a point in the centre of the circle that is traveling. Draw the line that point takes, and then calculate using the new circle.
- HarHarVeryFunny 3y ago
  Yes - the relationship between distance traveled by center and number of rotations (= distance/diameter) is a nice generalization, although the guy in the video went so fast that I didn't understand his derivation of this relationship (related to speed, etc).

HenryPrickett 3y ago

Very basically, to go the same direction, a small disk on the inside and the outside of a large disk need to spin opposite directions. When you're on the outside, your spinning direction agrees with the direction you go around the circle (i.e. the rotations add). When you're on the inside your spinning direction is the opposite of the direction you go around the circle (the rotation subtracts).

ahepp 3y ago

It’s concave rather than convex? It’s bending into itself instead of away from itself?

7734128 3y ago

You're intuitively rolling the other way. Going on the surface means that you're falling forwards while going inside means that you're falling backwards.

icegreentea2 3y ago

I think you can always arrive at the correct answer by tracking the distance traveled by the center of the rolling object. In the original SAT question, the center of the rolling circle is 4r from the center. That means it travels an arc of 8pi. Then assuming no-slip, that works out to 4 rotation. In your case, rolling on the inside, the center of the rolling circle will only be 2r from the center. Using the same logic, this yields 2 rotations.

bearmode 3y ago
This is definitely the easier way to understand it. Imagine a point in the centre of the circle that is traveling. Draw the line that point takes, and then calculate using the new circle.
HarHarVeryFunny 3y ago
Yes - the relationship between distance traveled by center and number of rotations (= distance/diameter) is a nice generalization, although the guy in the video went so fast that I didn't understand his derivation of this relationship (related to speed, etc).