Homework Help: Help with rotation of rigid bodies

1. Nov 8, 2004

RussG

Alright, I'm stuck on this problem.

Two metal disks, Radius 1 = 2.5cm, Mass 1 = 0.8kg and Radius 2 = 5.0cm, Mass 2 = 1.6kg are wielded together and mounted on a frictionless axis through their common center.

The first part asked what is the total moment of inertia of the two discs, which I got and it was 2.25 x 10^-3 kgm^2

Part b attaches a string to the smaller disk holding a cylinder of mass 1.5kg 2m above the ground. It asks the velocity of the cylinder right before it hits the ground when it's released from rest.

Then it moves the string in part c to the larger disc. I have the solutions but am not getting the same answers when I attempt to solve for it. I know that when attached to the larger disc it will have a greater speed because of the greater mass since their radiuses do not matter.

I have tried using the good ol K1 + U1 = K2 + U2 to determine its velocity.

I know K1 at rest is 0, and U1 is mgh. I know U2 is 0. So I need the final kinetic energy, right? Well the final kinetic energy would be 1/2mv^2 + 1/2Iw^2, or am I getting something wrong here?

since w = v/R I substituted that in.

I get 1/2(1/2MR^2)(v/R)^2 + 1/2mv^2 = mgh

solving for v I get sqrt((2gh)/(1+M/2m)) = v

Plugging in the numbers I'm not coming up with the correct velocities. Where have I gone wrong? Thanks for any help!