## Author(s)

## Publication date

2016-02

## Publisher

American Association of Physics Teachers

## Document type

## Abstract

We present an apparent paradox within the special theory of relativity, involving a trolley with
relativistic velocity and its rolling wheels. Two solutions are given, both making clear the physical
reality of the Lorentz contraction, and that the distance on the rails between each time a specific point
on the rim touches the rail is not equal to 2
p
R
,where
R
is the radius of the wheel, but
2
p
R
=
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
R
2
X
2
=
c
2
q
,where
X
is the angular velocity of the wheels. In one solution, the wheel radius
is constant as the velocity of the trolley increases, and in the other the wheels contract in the radial
direction. We also explain two surprising facts. First that the shape of a rolling wheel is elliptical in
spite of the fact that the upper part of the wheel moves faster than the lower part, and thus is more
Lorentz contracted, and second that a Lorentz contracted wheel with relativistic velocity rolls out a
larger distance between two successive touches of a point of the wheel on the rails than the length of
a circle with the same radius as the wheels.

## Version

publishedVersion

## Permanent URL (for citation purposes)

- http://hdl.handle.net/10642/4641