Minimum velocity for hoop rolling up a step without slipping

[Wen]

A hoop pf radius r and mass m is rolling without slipping with velocity v towards a step of height h on a horizontal surface. Assume that it does not rebound and no slipping occur at the point of contact when the hoop roll up, what is the minimum velocity needed for the hoop to roll up?



I tried to use conservation of energy to solve:
Ek(transl.)i +EK(rotat.)i=mgh+(Torque.change in angle of rotation)
1/2 mv^2 + 1/2 I w^2 = mgh + T.ditre
...
1/2 mv^2 + 1/2 mr^2(v^2/r^2)= mgh + m(r^2).(angu. acele)(ditre)
v^2=3/2 gh

this is far from the correct answ of 2r(gh)^0.5/(2r-h)

Please help me

 

[Tide]

The correct answer doesn't look quite right either. If h = r then the hoop won't make it up the step at any speed.

In any case, only the component of velocity perpendicular to a line joining the corner of the step and the center of the hoop can contribute to lifting the hoop.