200m vs 400m track

At some point as you slow the centrifugal force becomes so slight that you no longer have to have a centripetal force to balance it. With each track(bank pitch etc)and each person(center of mass etc)it varies but Id say for all it's when you run slowly enough to not "climb the banks" on the turn. To get a conversion factor to use is all but impossible.

The answer to the original question is that it depends heavily on the lengths of the respective turns. There is no such thing as centrifugal force. I could not let that go because it irritates me every time someone mentions it. In circular motion there is no outward seeking force. In the case of the person running 400 meters in 75 seconds (speed of 5.33 m/s) let's consider two cases: a 400 meter track with 100 meter turns and a 200 meter track with 50 meter turns. Now what provides the force in circular motion is the centripetal force. Centripetal force is equal to the mass of the object, times the square of the speed, divided by the radius, and is always directed toward the center of the circle. (To determine the centripetal acceleration, just eliminate the mass from the equation.) I will spare you some of the math, but the 200 meter track would have a radius of 15.9 meters and the 400 meter track a radius of 31.8 meters. Plugging these values into the acceleration leads to 1.787 m/s/s for the 200 meter track and .893 m/s/s for the 400 meter track. Thus in this case the runner/track would have to supply double the force to allow the runner to stay on the inside of the 200 meter track as would be necessary for the 400 meter track. Obviously, the faster the runner goes the harder it is for this force to be provided by a flat runner/track combination (thus banking indoors), but also the longer the radius of the turn the easier it is to run.

Thanks for that. It's what I knew to be true but I never bothered whipping out my calculator. My basic question might be better rephrased as "If you do a bunch of repeats on a 200 meter track, do you expect them to be just as fast as on a 400 meter track, and if not, what do you find to be a reasonable fudge factor?" Around this time of year I sometimes do workouts indoors and sometimes outdoors depending on weather. I've never attached a number to it, but whatever I do indoors I can match or better outdoors (unless it's very windy).

JimFiore wrote:

Around this time of year I sometimes do workouts indoors and sometimes outdoors depending on weather. I've never attached a number to it, but whatever I do indoors I can match or better outdoors (unless it's very windy).

Well, you just mentioned one of the factors in your own post. Wind. Certainly, when doing any repeats above 100m on a track, wind plays a factor...?

Thanks stunna. I am not up on changing sciences. My 40 plus years ago physics is rusty. I had always thought that it existed,as defined by my 1975 Merriam Webster the force that tends to impel a thing or parts of things outward from a center of rotation 2: the force that an object moving along a circular path exerts on the body constraining the object and that acts outwardly away from the center of rotation

I'll have to up date my books and my thinking.Does this force no longer call cetrifugal have a new name or was the science faulty. Hey That dusty old Big Bang thing was cutting edge thinking back in my youth.

Since the days of Isaac Newton, it's NEVER been centrifugal. Here's how things work, as conceptualized by him.

Objects travel with the same motion forever, unless/until some force acts on them to accelerate them. That concept is called inertia. It means that if an object is going in a circular path, it must constantly be acted on by a force directed towards the center: a CENTRIPETAL FORCE. Otherwise, it'd just travel in a straight-line path, instead of constantly turning to follow a circular path.

But here's where "centrifugal force" comes from. People notice that they tend to move away from the center; this isn't caused by a force, but by their previous motion, continuing to exist and take them away from the center.

An object HAS NO FORCE IMPELLING IT OUTWARD FROM THE CENTER OF ROTATION! Its inertia will carry it outward, since it's moving in a direction tangent to the circular path. However, it's being constantly accelerated by a centripetal force back inward, keeping it around.

I think the confusion comes from the usage of a centrifuge (as in chem lab).

But in any case, I take it no one uses a fudge factor between their 200/400 tracks.