 # 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? 11 years ago

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.......