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June 7th, 2014, 05:52 AM   #1
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Differential Speed

This may need to be in a different forum.... and may lead to a wager

So we're in a poker game, and a guy poses a problem:

A car is going 60 mph in a straight line, point A to point B. The car has 16" tires. Imagine a white dot painted on the outside of one of the tires. How fast is the spot going?

Clearly, in one plane, the spot is going 60 mph (it will arrive at point B at exactly the same time as a similar spot painted directly above it on the fender). But the spot on the tire is also travelling up and down so it must in some sense be going faster than the car.

Do we first need to define speed/fast?

Then there was the question about the speed of the track on a moving tank, but we'll try that one later.

It's a helluva poker game (I'm more the group philosopher than mathematician).

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June 7th, 2014, 03:52 PM   #2
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76.4 mph.

Last edited by greg1313; June 7th, 2014 at 04:35 PM.
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June 7th, 2014, 04:37 PM   #3
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240 mph.
Hey, I know it's not my question but I like to read everyone's answers so would be nice to know how you actually have that answer with a brief explanation.

oops changed your answer. I still think that the car can only travel as fast as the wheel is going, which happens to be at 60.m.p.h, the dot is not going up and down but round and round which is actually just the dot going forward isn't it?

this is why explanations a re good simpletons like me

Last edited by nmenumber1; June 7th, 2014 at 04:40 PM.
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June 7th, 2014, 04:50 PM   #4
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See this page.

The arc length of the cycloid is 8 times the radius and the car travels 16 * pi inches per tire revolution
so the ratio between the two speeds is about 1.2732.
1.2732 * 60 ≈ 76.4.
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June 7th, 2014, 05:06 PM   #5
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wow that's awesome thanks very much
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June 7th, 2014, 05:16 PM   #6
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The spot doesn't travel at a constant speed. Indeed, when it's at the bottom of the tyre, it is stationary (unless the brakes are locked up or the wheels are spinning).
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June 7th, 2014, 05:23 PM   #7
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I'm not sure I agree with that. The tyre is in constant motion.
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June 7th, 2014, 06:11 PM   #8
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Had to think about that!
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June 7th, 2014, 06:41 PM   #9
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Had to think about that!
Yes, it's rather counter-intuitive, but if the tyre is gripping either the spot is stationary or the road is moving. Your choice.
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June 8th, 2014, 01:10 PM   #10
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When the spot is at the top , it's going 120mph, vroom! (relative to the road)
When the spot is at it's most forward or most rear it is matching the speed of 60mph.
Tank tracks aren't really any different.
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