ω2r = vrdvdr
integrate both sides ( vr = radial vel )
(ωr)2 = vradial 2
vradial = rw =drdt
again integrate
[lnr] = [wt] , t=0 , r = ro
so r = roeωt
at any r , torque of normal abt hinge, = rate of change of ang momentum abt that hinge
Nr = dLdt = ddt (mr2ω ) = 2mrω (vr )
so N = 2mω(vr ) = 2mω (rω) = 2mω2roeωt
so net normal = √ (2mω2roeωt )2+(mg)2