Finding moment of inertia of a cylinder with a falling mass

[dross]

Hi I am struggling with the following question.

A cylinder of radius 20cm is mounted on a horizontal axle coincident with its axis and is free to rotate. A light chord is wound onto it and a 50g mass hung from it. After release the mass drops 1m in 12seconds. What is the moment of inertia?

With energy conversation I know the gravitational potential energy lost must equal that of the kinetic energy gained my the mass + the rotational energy gained by the cylinder

0.5mv^2+0.5Iω^2 = mgh

I can rearrange this to find moment of Inertia, I. However is ω = v/r ? with v being 1/12 m/s ?

 

[Merlin3189]

v is not 1/12 m/s. The average speed is 1/12 m/s, but since it starts from rest, the final speed must be higher.
Otherwise you seem on the right track.

 

[dross]

Yep got it. Thanks for your help!