Notice that there is a nice linear relationship between the square position of the wheel and the horizontal position? The slope of this line is 0.006 meters per step. If you had a wheel with a larger radius, it would move a greater distance for each rotation – so this slope seems to have something to do with the radius of the wheel. We wrote this as the following phrase.
In this equation, s the speed at which the center of the wheel moves. The radius is r and the square position is θ. That just goes away k– this is just sustainable. Since then s Vs θ is a serial function, kr it must be the slope of that line. I already know the value of this slope and can measure the radius of the wheel to be 0.342 meters. With that, a k value 0.0175439 with units of 1 / degree.
Great deal, right? No, it is. Check this out. What happens if you multiply a value k ro 180 degree? For my value of k, I get 3.15789. Yes, that’s actually TRUE close to the value of pi = 3.1415 … (at least that’s the first 5 branches of pi). Seo k as a way to convert from square units of degrees to a better unit for measuring angles – this new unit is called a radian. If the angle of the wheel is measured in radians, k it equals 1 and you get the following loving relationship.
There are two important elements in this equation. First, technically pi is in there because the angle is in radian (yay for Pi Day). Secondly, this is how a train stays on the route. Seriously.