Keywords: Centripetal force vs external force vectors.svg en Shows in the upper half the position of a valve of a wheel seen from the reference frame Street -> Cycloid In black the position in x-y plane in red the instantaneous velocity of the valve in green the inst acceleration Lower part The decomposition of the external force left side of newton 2 Blue tangent component tangent to the instantaneous circle of curvature of this force Yellow centripetal component own Svebert Source Code Created with Matplotlib <source lang 'python'> Script to produce this figure python from math import import numpy as np import matplotlib pyplot as plt tarr np linspace -1 0 3 pi 400 xarr np zeros len tarr yarr np zeros len tarr vxarr np zeros len tarr vyarr np zeros len tarr axarr np zeros len tarr ayarr np zeros len tarr apxarr np zeros len tarr apyarr np zeros len tarr aZpxarr np zeros len tarr aZpyarr np zeros len tarr aFZp np zeros len tarr aF np zeros len tarr i 0 R 2 0 r R omega 1 0 for t in tarr xarri R omega t-r sin omega t yarri R-r cos omega t i+ 1 vxarr np diff xarr vyarr np diff yarr axarr np diff vxarr ayarr np diff vyarr Kruemmungsradius vsquared for i in range len tarr -2 v2 vxarri vxarri+vyarri vyarri av vxarri axarri+vyarri ayarri apxarri av vxarri/v2 apyarri av vyarri/v2 aZpxarri axarri-apxarri aZpyarri ayarri-apyarri aFi sqrt axarri axarri+ayarri ayarri aFZpi sqrt aZpxarri aZpxarri+aZpyarri aZpyarri plt figure plt subplot 211 aspect 'equal' adjustable 'box' title 'Reference frame Street velocity and acceleration' plt plot xarr yarr 'k' plt hold 1 plt quiver xarr 20 yarr 20 vxarr 20 vyarr 20 color 'r' label 'velocity' plt hold 1 plt quiver xarr 20 yarr 20 axarr 20 ayarr 20 color 'g' label 'acceleration' plt ylim 0 max yarr plt xlim 0 max xarr plt axes set_aspect 'equal' pl show plt axes set_aspect 'equal' plt subplot 212 aspect 'equal' adjustable 'box' title 'Reference frame Street Tangent and Centripetal Force' plt figure plt plot xarr yarr 'k' plt hold 1 plt quiver xarr 20 yarr 20 apxarr 20 apyarr 20 color 'b' plt quiver xarr 20 yarr 20 aZpxarr 20 aZpyarr 20 color 'y' plt ylim 0 max yarr plt xlim 0 max xarr plt savefig 'centripetal_force_vs_external_force_vectors svg' plt axes set_aspect 'equal' plt show plt figure plt title External Force tangent and centripetal components plt plot axarr ayarr 'g' label 'External Force' plt hold 1 plt plot aZpxarr aZpyarr 'y ' label 'Centripetal Force' plt plot apxarr apyarr 'b ' label 'Tangent Force' plt ylim min min ayarr min aZpyarr min apyarr max max ayarr max aZpyarr max apyarr 1 6 plt legend plt axes set_aspect 'equal' plt savefig 'centripetal_force_vs_external_force_circles svg' plt figure plt title 'External Force and centripetal component vs time' plt hold 1 plt plot tarr aFZp 'y' label 'centripetal component' plt plot tarr aF 'g' label 'External Force' plt legend loc 'lower left' plt xlim 0 tarrlen tarr -3 plt savefig 'centripetal_force_vs_external_force_time_series svg' plt show </source> Cycloid Inertial forces Centripetal force Cc-zero |