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File:Ehrenfest-paradox-disk.svg

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Original file (SVG file, nominally 220 ×ばつ 180 pixels, file size: 4 KB)
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Summary

DescriptionEhrenfest-paradox-disk.svg
English: The Ehrenfest paradox in special relativity describes a spinning cylinder, which should contract around the circumference due to Lorentz-contraction, while its radius remains constant. The graphic shows rulers which rest in the laboratory system and rulers attached to the cylinder, which get contracted relatively to the laboratory system.
Deutsch: Das Ehrenfestsche Paradoxon der Speziellen Relativitätstheorie beschreibt einen rotierenden Zylinder, der sich entlang seinem Umfang aufgrund der Lorentzkontraktion kontrahieren sollte, während sein Radius konstant bleibt. Die Grafik zeigt Maßstäbe die im Laborsystem ruhen, so wie Maßstäbe die mit dem Zylinder rotieren und deshalb relativ zum Laborsystem kontrahiert werden.
Date
Source Own work
Author Geek3
Other versions Spinning-disk.svg (without rulers)

Source Code

The image is created by the following source-code. Requirements:

python source code: 

#!/usr/bin/python
# -*- coding: utf8 -*-
try:
 importsvgwriteassvg
except ImportError:
 print 'You need to install svgwrite: http://pypi.python.org/pypi/svgwrite/'
 exit(1)
frommathimport *
size = 220, 180
rx, ry = size[0] / 2 - 3, 50
v = float(ry) / float(rx)
l = 40
lw = 2
# document
doc = svg.Drawing('ehrenfest-paradox-disk.svg', size=size)
doc['stroke-width'] = lw
doc['fill'] = 'white'
doc['stroke'] = 'black'
doc['stroke-linejoin'] = 'miter'
# background
doc.add(doc.rect(id='background', insert=(0, 0), size=size, stroke='none'))
# disk
grad = doc.defs.add(doc.linearGradient(id='grad', start=('0%',0), end=('100%',0), gradientUnits='objectBoundingBox'))
grad.add_stop_color(offset=0, color='#f7f7f7')
grad.add_stop_color(offset=0.5, color='#dddddd')
grad.add_stop_color(offset=1, color='#999999')
disk = doc.add(doc.g(id='disk', transform='translate(' + str(size[0]/2) + ',' + str(ry+3) + ')'))
path = 'M ' + str(-rx) + ',0 V ' + str(l)
path += ' A ' + str(rx) + ',' + str(ry) + ' 0 1 0 ' + str(rx) + ',' + str(l)
path += ' V 0 Z'
disk.add(doc.path(d=path, fill='url(#grad)', stroke_linejoin='bevel'))
disk.add(doc.ellipse(center=(0, 0), r=(rx, ry), fill='#d8d8d8'))
disk.add(doc.ellipse(center=(0, 0), r=(2, 2.0*v), fill='black'))
radius_angle = radians(-40.0)
csr = cos(radius_angle), sin(radius_angle)
disk.add(doc.line(start=(0,0), end=(rx*csr[0], ry*csr[1]),
 stroke_width=lw*sqrt(csr[0]**2 + (v*csr[1])**2)))
# round arrow
ar, aw, ah, ab, al, a0, a1 = 0.7*rx, 7, 2, 1, 3, radians(160), radians(100)
apath = 'M ' + str(ar*cos(a0)) + ',' + str(ar*sin(a0))
apath += ' A %f,%f 0 0 0 %f,%f' % (ar, ar, ar*cos(a1), ar*sin(a1))
arrowhead = doc.defs.add(doc.marker(id='arrowhead', orient='auto', overflow='visible'))
arrowhead.add(doc.path(fill='black', stroke='none',
 d='M 0.0,0.0 L %f,%f L %f,0 L %f,%f L 0,0 z'%(-ab, -ah, al, -ab, ah)))
arrow = doc.path(d=apath, fill='none', stroke_width=aw, transform='scale(1,' + str(v) + ')')
arrow['marker-end'] = arrowhead.get_funciri()
disk.add(arrow)
# ruler
ruler = doc.defs.add(doc.g(id='ruler'))
rw, rh, rn = 32, 14, 4
ruler.add(doc.path(d='M 0,0 H %f V %f H 0 V 0 Z'%(rw+3, rh),
 fill='white', stroke='none'))
squares = ''
for i in range(rn/2):
 squares += 'M %f,0 H %f V %f H %f V 0 Z '%(i*rw*2./rn, (1+i*2.)*rw/rn, rh, i*rw*2./rn)
ruler.add(doc.path(d=squares, fill='red', stroke='none'))
ruleredge = 'M %f,0 H %f V %f H 0 V 0 H %f V %f'%(rw, 3+rw, rh, rw, rh)
for i in range(1, rn):
 ruleredge += ' M %f,0 V %f'%(i*rw/float(rn), rh/2.)
ruler.add(doc.path(d=ruleredge, fill='none', stroke='black', stroke_width=lw, stroke_linecap='round'))
rulers = doc.add(doc.g(id='rulers'))
rulers.add(doc.use(ruler, insert=(0, 0), transform='matrix(0.89, 0.42, 0, 1, 17, 134)'))
rulers.add(doc.use(ruler, insert=(0, 0), transform='matrix(1.00, 0.16, 0, 1, 54, 150)'))
rulers.add(doc.use(ruler, insert=(0, 0), transform='matrix(1.00, 0.00, 0, 1, 95, 156)'))
rulers.add(doc.use(ruler, insert=(0, 0), transform='matrix(0.53, 0.33, 0, 1, 16.53, 91)'))
rulers.add(doc.use(ruler, insert=(0, 0), transform='matrix(0.57, 0.19, 0, 1, 39, 104)'))
rulers.add(doc.use(ruler, insert=(0, 0), transform='matrix(0.60, 0.10, 0, 1, 63, 112)'))
doc.add(doc.path(d='M 16.5,106 V 133', fill='none', stroke_width=1, stroke_dasharray='4,2'))
doc.add(doc.path(d='M 84.5,130 V 154', fill='none', stroke_width=1, stroke_dasharray='4,2'))
# text
doc.add(doc.path(id='omega', stroke='none', fill='black',
transform='translate(70,70) scale(0.03,-0.03)',
d='M 13 0 m 251 82 c 9 -63 43 -93 94 -93 c 59 0 113 38 153 93 c 75 104 94 \
255 94 289 c 0 71 -37 71 -43 71 c -25 0 -50 -26 -50 -48 c 0 -13 6 -19 15 -27 \
c 32 -33 35 -65 35 -87 c 0 -85 -85 -219 -190 -219 c -9 0 -37 0 -55 23 c -12 \
16 -20 35 -20 55 c 0 3 0 5 6 16 c 19 45 33 100 33 113 c 0 12 -7 23 -21 23 c \
-11 0 -20 -9 -28 -25 c -2 -5 -14 -49 -21 -101 c -2 -18 -2 -20 -9 -27 c -44 \
-61 -90 -77 -124 -77 c -66 0 -88 55 -88 114 c 0 75 37 158 84 225 c 10 14 10 \
16 10 19 c 0 8 -6 12 -12 12 c -16 0 -62 -88 -76 -120 c -37 -89 -38 -171 -38 \
-180 c 0 -80 30 -142 106 -142 c 65 0 113 46 145 93 z'))
doc.add(doc.path(id='r', stroke='none', fill='black',
transform='translate(152,60) scale(0.03,-0.03)',
d='M 29 0 m 59 59 c -3 -15 -9 -38 -9 -43 c 0 -18 14 -27 29 -27 c 12 0 30 8 \
37 28 c 2 4 36 140 40 158 c 8 33 26 103 32 130 c 4 13 32 60 56 82 c 8 7 37 33 \
80 33 c 26 0 41 -12 42 -12 c -30 -5 -52 -29 -52 -55 c 0 -16 11 -35 38 -35 c \
27 0 55 23 55 59 c 0 35 -32 65 -83 65 c -65 0 -109 -49 -128 -77 c -8 45 -44 \
77 -91 77 c -46 0 -65 -39 -74 -57 c -18 -34 -31 -94 -31 -97 c 0 -10 10 -10 12 \
-10 c 10 0 11 1 17 23 c 17 71 37 119 73 119 c 17 0 31 -8 31 -46 c 0 -21 -3 \
-32 -16 -84 z'))
doc.save()

Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:
[画像:GNU head] Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License , Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License .http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue
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  • to share – to copy, distribute and transmit the work
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Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
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21 January 2013

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Date/TimeThumbnailDimensionsUserComment
current00:35, 21 January 2013 Thumbnail for version as of 00:35, 21 January 2013 220 ×ばつ 180 (4 KB)Geek3 {{Information |Description ={{en|1=Ehrenfest paradox illustration}} |Source ={{own}} |Author =Geek3 |Date ={{Date|2013|01|21}} |Permission = |other_versions = }}

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Short titleEhrenfest-paradox-disk.svg - Illustration of the Ehrenfest paradox in special relativity
Image titleThe Ehrenfest paradox in special relativity 
 (http://en.wikipedia.org/wiki/Ehrenfest_paradox) describes a spinning
 cylinder, which should contract around the circumference due to
 Lorentz-contraction, while its radius remains constant. The graphic shows
 rulers which rest in the laboratory system and rulers attached to the
 cylinder, which get contracted relatively to the laboratory system.

 from Wikimedia Commons

 about: http://commons.wikimedia.org/wiki/Image:Ehrenfest-paradox-disk.svg
 source: http://commons.wikimedia.org/
 rights: GNU Free Documentation license,
Creative Commons Attribution ShareAlike license
Width220
Height180

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