The moment of inertia of the turntable I 1=MRR/2, the moment of inertia of the tripod at the edge I2=mRR, and the moment of inertia I2'= mRR when its distance from the center of the turntable is r.

Both cases are conservation of angular momentum. The initial angular momentum of the system composed of turntable and spider is J=I 1*w+0=wMRR/2.

1) when the spider falls on the edge, the angular velocity of the turntable becomes w', and the angular momentum of the system is j' = (I1+I2) w' = w' (m/2+m) RR. From J=J': wMRR/2=w'(M/2+m)RR, so w'=w[M/(M+2m)].

2) When the distance between the spider and the center of the turntable is r, the angular velocity of the turntable becomes w ",and the angular momentum of the system is j" = (I1+I2') w "= w" (MRR/2+MRR). From J=J ":wMRR/2=w"(MRR/2+mrr), so w"=w[M/(M+2mrr/RR)].