an interesting problem I came along this problem, it is quite interesting. However, I have worked with the problem to long and than you can't see any new ways. So I thought, maybe you guys could try it with a fresh mind. Good luck, it is a tough one (or I fail to see something obvious) imagine a jojo on a string which can be represented by three clinders, the middle one(with the wire around it) with mass m1 and diameter/2(I don't know what that is in english, in dutch it is straal)R1, and the two cilinders on the sides of it both have mass m2 and R2. first give the rotational inertia on a horizontal axis through the center of mass point. that was easy, 1/2m1*r1^2+m2*r2^2. the second question was: calculate the accelaration when the jojo falls down( it rolls down the wire and the axis all stay in the same alignment). here I got stuck. I thought, you can analyse the movement as a pure rotation around the point where the wire is connected to the middle cilinder. then the angular momentum becomes 1/2m1*r1^2+m2*r2^2+(m1+2m2)*r1^2 (paralel axes law.) speed is then expressable as (m1+2m2)hg=1/2(Ip)W^2. However, if you fill this in and try to express the speed, you get a gigantic formula that can't be right. I must be taking a wrong route, after all, I need the acceleration, not the speed, but I don't know how to come there. Help would be greatly appreciated.(I am always a bit messy in my work, so it is possible that I made a mistake in the start of the answer) sorry for my poor english, especially on physics therms. faithfully, olympiad..