Sorry guys but uploading the image didnt work so i post it on imageshack. Here is the link: http://imageshack.us/f/208/apib.jpg/
So the quastion is:
In the image the pulley is a uniform cylindrical disk of mass m and radius r. The strings are massless and there is no friction. If the system is initially at rest, find the speed of the blocks after they have moved a distance d.
E = E + W
K = 1/2Iω^2
The Attempt at a Solution
Let's say that the potential energy is set at 0 when the blockmoves from y=d --> y=0.
Then the starting energy becomes (m1+m2)gh = 2mgd
Translating to kinetic energy, ΔU =(1/2)(2m)v2 - (1/2)Iω2
Because our pulley also has a mass m, and I =(1/2)mr2
ΔU = mv2 -(1/4)m(r2ω2) = mv2-(1/4)mv2 (Using v =rω)
So ΔU = (3mv2)/4 = 2mgd
And my answer is:
My book say the answer is : v =√[(4gd)/5]. So im wondering what im doing wrong?