Angular momentum/angular velocity.

[the whizz]

Homework Statement

1.A solid, vertical cylinder of mass 10.0 kg and radius 1.00 m rotates with an angular speed of 7.00 rad/s about a fixed vertical axis through its center. A .250 kg piece of putty is dropped vertically onto the cylinder at a point 0.900 m from the center of ration and sticks to the cylinder. Determine the final angular speed of the system.

Homework Equations

Lbefore=Lafter
L=Iw

The Attempt at a Solution

the angular momentum is L and the angular velocity is what i am looking for that is w.
I believe you can say that IoWo should = IW

I am unsure what you are to do with the mass of the putty and the center of radian issue.

I believe you need to set up taht W = (Io/I)wo

Io = MR^2?

 

[glueball8]

$$I_{o}\times \omega_{o}=I_{f}\times \omega_{f}$$

We know $$I_{o}= \frac{1}{2}MR^2$$ plus we know wf

$$I_{f}=\frac{1}{2}MR^2+mr^2$$
Note: the $$I_{f}$$ changes, the parallel axis theorem is used.

only $$\omega_f$$ left that's unknown.