a small hoop of mass m is given an initial velocity of magnitude v on the horizontal circular ring of radius r. if the coefficient of kinetic friction is u the tangential acceleration of hoop immediately after its release(assume horizontal ring to be fixed and not in contact with any supporting surface)
force acting at the center of hoop are:
normal force N upwards,
mg downwards
ac towards centre=v0^2/R
F=coeff. of kinetic friction . N
N=(m^2g^2 +m^2 v0^4/R^2)^1/2
therefore tangential acc. =F/m= u.(g^2 + v0^4/R^2)^1/2
normal force N upwards,
mg downwards
ac towards centre=v0^2/R
F=coeff. of kinetic friction . N
N=(m^2g^2 +m^2 v0^4/R^2)^1/2
therefore tangential acc. =F/m= u.(g^2 + v0^4/R^2)^1/2