Thoughts

It looks like Nathan S. already has our answer:

The trick is to distort the problem enough and it becomes apparent what is going on.

Normally you might think of the inside lane having a radius of 40' and the outside lane having a radius of 50'. The differences are small, so it's hard to think about what is happening. Imagine, though, that the inside lane has a radius of 10' and the outside lane has a radius of 10 miles.

Obviously the outside lane is much, much longer, meaning a shallower curve, and a much faster speed. Of course it will take you longer to complete the outer circle, and the additional speed isn't guaranteed to offset the differences in length.

The speed that you can travel will only increase with the radius of the circle, so the same logic holds for any two lane radii. But, in real life this is also influenced by the slope of the curve. If the inside lane is sloped (inward) more than the outside lane, it will make a difference and could change which lane is faster.
 

i guess i haven't physics since high school, and toby choy can attest to the fact that i slept through most of it. that might explain why i totally don't understand nathan's answer at all. haha.
 

Basically, in English:

You would drive faster on the outside lane because the turn radius is wider (sharper turns by the inside lane would reduce the car's speed).

But the steeper the inward slope of the lanes, the faster the car would travel.
 

you can go just as fast on either. you can choose to go 50mph on an inside lane just as much as you can choose to do so on an outside lane. This is true regardless of how big or small the curvature and distance is.

Say it's a complete circle and the inner lane's circumference is 10 miles and the outer lane, say, is 10000000 miles... Let's even blow it out of proportion and compare this to stars orbiting vs. an airplane going around the earth.

insade lane= planet traveling around the earth
outside lane= sun revolving around the earth.

For argument's sake, let's say they are both going 100mph.

Speed, defined as distance over time, is identicle. Therefore, you can go just as fast (fast= speed= miles per hour in this case) whether or not you are in the inner or outler lane.

Now bring this back to proportion and the same holds true for the inner lane of a vehicle lane and the outer lane.
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However, that's just the SPEED.

When you take centripetal force into account, you will feel more force if you are in the inner lane. You can probably picture this in your mind. if you were going 50 mph and going along a curve where you had to turn your wheels to the right at a 3 o'clock angle continuously, you'd be leaning in severly toward the center of the curve. If you were on the outside of the lane and STILL going 50mph but only had to tilt your handle to the right at a 12:30 angle on the clock just to make the same curve on that lane, you can imagine that you'd hardly feel like you're being violently swayed toward the center of that curve.

Therefore, even though both cars would be still going at 50mph, you'd FEEL like you're going faster at the inner lane because of the greater centripetal force. No?

Also to explain mathematically, the time it would take to complete the circle will obviously be shorter in the inner lane because time = 2(pi)(Radius)/velocity.

Well, this time it takes is also used to calculate the angular rate of rotation which = 2(pi)/time it takes to complete the circle.

So obviously, the inner lane has a smaller time than the outer time. Put that into account when the T is in the denominator, the angular rate of rotation is greater for the inner lane than it would be in the outerlane.

Hence, you can still go the same velocity on both lanes, but the angular rate of rotation you feel is much greater in the inner lane and you'd FEEL like you're going faster because you're being jerked toward the center of the curvature at a more intense rate.