borut wrote:If you dont mind I will fight you on this one for a while.

Sure, be my guest
borut wrote:OK But hypotenuse is crossing the arc. You can not move like that.
Is Miles' suggestion any better - moving in zigzags?

No, of course, you're moving smoothly along the arc. That's why I mean an arc is just a bent straight line, not made up of zigzag movements. The turning is happening constantly, but can be viewed "per time unit" as tangents or "per time segment" as hypothenuses (shorter = more accurately, longer = less than the actual arc). This constant turning could be caused by e.g. a car's stearwheel at a set position or a carousel wagon constraint to a metal arm (constant radius).
borut wrote:Now if object has velocity and we measure the time it needs to travel around the circle in a way that is mechanically possible, what time it needs to go around? We all know that distance is defined by time and velocity. Is that objects velocity constant?
The reasoning is kind of backwards, but this could be quite easily tested. One way would be to drive a car in constant speed in a predefined circular path on an empty parking lot
(make path e.g. by using a long rope straight from a center and place small objects along the path). Then compare the time it takes per loop, with the calculus. I don't see any reason why the loop time measured shouldn't equal: t = d / v -> t = 2*pi*r / v (pi = 3,14159...)
If the car's speed is 20 km/h (5,56 m/s) and the path's radius is 10 meter, then you'll get:
t = (2 * 3,14159 * 10) / 5,56 = 11,30 s
Versus pi = 4:
t = (2 * 4 * 10) / 5,56 = 14,39 s
Any volunteering testers? Any bets?

Some anomalies due to stearing/speed inaccuracies, of course. Other ways of testing that I could think of involves too much friction, deceleration or gravity.