Angular Momentum of Clay & Cylinder: Find Rotational Speed

[thenewbosco]

(Diagram http://snipurl.com/couf )

A wad of sticky clay (mass m, velocity v), is fired at a solid cylinder (mass M, radius R). The cylinder is initially at rest and rotates on an axis through the center of mass. The line of motion of the projectile is perpendicular to the axis of rotation and at a distance d < R from the center.


Find the angular speed of the cylinder just as the clay hits the surface.

I am trying to use conservation of momentum to solve this.
we can say, i suppose, that :

L_{clay final}-L_{clay initial} = L_{cylinder final} [/itex]<br /> <br /> Now i have know idea what to substitute for these values. I know <br /> L= R x mv, or for the rotating cylinder L=Iw, but for the initial angular momentum of the clay, do i find R? Somehow, d ends up in the final answer. Can someone show me the correct way to set this one up.<br /> <br /> Thanks

 

[dextercioby]

Yes,i assume that the law of conservation of angular momentum should be enough to do it.
1.What is the total angular momentum of the system at the initial moment of time??

Daniel.

 

[thenewbosco]

"1.What is the total angular momentum of the system at the initial moment of time??"


It should just be the angular momentum of the clay, which would be
r x mv, (isnt that correct), but the radius r is what i do not know. I assume somehow that d factors in there somehow since there is a d in the final answer.

 

[thenewbosco]

wait i think i have something, the initial r is d/sin theta, and that sine of theta will cancel out with the sine of theta in the cross product. This might work.
but for the two final values i don't know.

 

[thenewbosco]

Hey, i got the answer, thanks for you help though.