Angular momentum uniform rod problem

[HobieDude16]

well, I've tried, and I've tried, but i can't seem to get this one right, my TA did it in class, but left something out i think, he did it in a big hurry, so i can't get an answer that's right... ill show you what I've tried, and maybe you can spot my error? any help is much appreciated

Figure 11-49 is an overhead view of a thin uniform rod of length 0.600 m and mass M that is rotating horizontally at 80.5 rad/s counterclockwise about an axis through its center. A particle of mass M/3.00 and speed 41.5 m/s hits the rod and sticks. The particle's path is perpendicular to the rod at the instant of the hit, at a distance d from the rod's center.

(a) At what value of d are rod and particle stationary after the hit?
m


ok, so our ta worked out the cross produt of r and the particle, and used that to get the equation (1/12)mL^2 omega^2-d(m/3)v=0... so you sove that out, and get d=(L^2omega^2)/4v but that's just not right... what am i doing wrong? any help? thanks in advance
John

 

[HobieDude16]

somebody has to have SOME ideas... come on guys...

 

[HobieDude16]

i guess nobody knows how to do it, at least I am not the only one

 

[Phymath]

well i don't think u wrote down what ur TA wrote correctly

$$L = d * p = d(M/3)v$$ cause its perp to the rod
$$L = Iw = \frac{1}{12}ML^2w$$

$$\frac{1}{12}ML^2w - d(M/3)v = 0$$
$$d = \frac{L^2w}{4v} = 0.175m$$

u don't square the angluar velocity I am not sure why u had that..

 

[HobieDude16]

maybe i did, but i think it was cause he was in a hurry, he did it in less than 2 minutes, cuase we had to take a quiz before we left, but either way, thanks for the help man, stupid mistakes always hurt : (

 

[Phymath]

glad to help!

 

[HobieDude16]

thnk you could help on that other one i posted down lower, about variables? cause that one I've racked my brain on for a while... still no result though... you seem to know this stuff pretty well too

 

[Phymath]

post a link

 

[HobieDude16]

hahah, nevermind, gingerbread helped me out... i was overlooking the obvious, but thanks for the offer!