Re: Do people in back of a roller coasters move faster than people at front?

A very interesting question, and one that I have asked myself many times 
while on roller coasters!  And you have actually supplied the answer!


Since all the cars of the roller coaster are more or less rigidly connected 
(they can't move forward or backward independently of the other cars) all 
the cars in the train of the roller coaster have the same speed at the same 
time.  In addition, there is no acceleration difference between riding in 
the front car versus the back car.  But we do feel a difference, which I 
will describe in the next paragraph.


What we actually experience as being different between the front car and 
the back car is our expectations of the accelerations we think we should be 
feeling.  The entire train of the coaster experiences accelerations 
(changes in speed) according to the position of the center of mass of the 
train, which we can think of as being somewhere near the middle of the 
train.  When we are in the front car and go over the edge of a hill we 
think we ought to be accelerating already, but the center of mass has not 
yet gone over the edge of the hill and so we feel as if we are going slower 
than we ought to be going.  In the back car the center of mass has gone 
over the edge before we do and so we experience an acceleration sooner than 
we expect, which makes it feel like we are going faster.


I have analyzed this many times while on a roller coaster, and I am sure 
that I am correct.  My family thinks I'm crazy trying to analyze something 
while I'm supposed to be having fun!  But I have fun in two ways:  
experiencing the roller coaster and also figuring out what makes it feel 
the way it does!!