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A sphere is rolling without slipping on a rough surface..Is there is arrangement done which can nullify the effect of friction i.e. altough friction is there, no force due to ftiction acts on it while rolling?
consider a sphere rolling on a frictious surface......
A force F is acting on the sphere horizontally ,r distance above the center of sphere....
friction force will be in foreward direction and let it be f ..
now we have ,
f + F = ma...........1 (for translational motion)
and
F r- fR = I(angular accleration) ,
(for rolling without slipping, a=(angular accleration)R)
Fr - fR = Ia/R (R is radius of sphere and I is moment of inertia of sphere)
or Fr - fR= 2MaR/5 (I for sphere is 2MR2 /5)
or F - fR/r = 2MaR/5r ............2
eq 1 - eq 2
f(1+R/r) = Ma(1-2R/5r)
f= Ma(1-2R/5r) /1+R/r
now f = 0 when r =2R/5
therefore when a force acts on the sphere at a distance 2R/5 above the center then sphere friction force acting on the sphere will be zero.......
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