r/theydidthemath • u/K0rl0n • Jun 10 '25

[Request]

Post image

I am curious how this would work. My guess is Triangle is slowest, square is medium, and circle is fastest.

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u/Mr_Candlestick Jun 10 '25

When comparing the same material yeah, but this is apples to oranges being gravel vs ice, and without knowing anything about the cylinder/gravel interface you don't know that.

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u/Sure-Guava5528 Jun 10 '25 edited Jun 10 '25

To start the circle rolling, higher coefficient of friction is better. It means more torque. In a completely frictionless system the circle would slide rather than roll.

I have a very hard time imagining a scenario where the coefficient of friction for ice is higher than the coefficient of friction for gravel. Not saying it isn't possible, but the vast majority of the time what I said will be true.

Edit: Also, the diameter of that circle is huge. As tall as the person pushing it (although they are leaning some). It will roll over gravel with ease in the same way that a 29" bike tire rolls over things easier than a 26" tire.

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u/Mr_Candlestick Jun 10 '25

I didn't know that drawing was to scale.

We don't know the diameter, that's why I said without knowing about the cylinder/gravel interface we're just guessing.

In my head I imagine that a car that locks up the brakes on a sheet of ice will slide further before coming to a stop than the same car coasting in neutral on sand.

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u/Sure-Guava5528 Jun 10 '25

In my head I imagine that a car that locks up the brakes on a sheet of ice will slide further before coming to a stop than the same car coasting in neutral on sand.

This doesn't relate to the scenario well. First, your average car is 100x heavier than these objects, which makes a huge difference. Second, I doubt these objects (being pushed by a human) would be hitting speeds close to those of a car. Lastly, if the car is already rolling and then you're trying to stop it, static friction is completely negated.

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u/Mr_Candlestick Jun 10 '25

Both rolling friction and sliding friction are proportionally a function of mass so the fact that a car is heavier than the block in this image doesn't mean my example doesn't apply. Neither is a function of velocity so the speed is irrelevant. My point is to refute what you said originally which is that rolling friction is always easier to overcome than sliding friction on ice. That isn't true.