Angular Momentum Conservation with a Parakeet Landing on a Turntable

[pelmel92]

Homework Statement

Consider a cylindrical turntable whose mass is M and radius is R, turning with an initial angular speed ω1.

(a) A parakeet of mass m, after hovering in flight above the outer edge of the turntable, gently lands on it and stays in one place on it, as shown below. What is the angular speed of the turntable after the parakeet lands? (Use any variable or symbol stated above as necessary.)
ωf = ? (b) Becoming dizzy, the parakeet jumps off (not flies off) with a velocity relative to the turntable. The direction of is tangent to the edge of the turntable and in the direction of its rotation. What will be the angular speed of the turntable afterwards? Express your answer in terms of the two masses m and M, the radius R, the parakeet speed and the initial angular speed ω1. (Use any variable or symbol stated above along with the following as necessary: v for ||.)
ωf = ?

Homework Equations

L=mvr+Iω
I(turntable)=.5MR^2
I=∑mr^2

The Attempt at a Solution

I had no issues with part one, and correctly found ωf to be equal to Mω1/(M+2m).
But I can't figure out where I've gone wrong with part two...

I thought that, due to the cons. of L, (.5MR^2 +mR^2)ω1= .5MR^2ωf +mvR
but solving for ωf in this equation keeps coming up wrong...

Am I missing something obvious? Any help would be greatly appreciated.

 

[zhermes]

Your equation looks right to me... what final answer did you end up with?

 

[pelmel92]

ωf= ω1 + 2mω1/M -2mv/(MR)

do i just suck at algebra?

 

[zhermes]

Wow, no that looks good [but I learned that I sure suck at algebra---from my first try... :( ].
Could your solutions be wrong?

 

[pelmel92]

hold on...thought i caught it but I'm still a bit confused here...

.5MR^2ω1 +mR^2ω1= .5MR^2ωf +mvR
so

.5MR^2ω1 +mR^2ω1 -mvR = .5MR^2ωf

and

(.5MR^2ω1)/(.5MR^2) +(mR^2ω1)/(.5MR^2) - (mvR)/(.5MR^2) = ωf
right?
which means that

ω1 +2(mω1)/M - 2(mv)/(MR) = ωf

maybe I'm just being dense but i can't see where i went wrong...

 

[pelmel92]

i guess that's always possible... it's a webassign homework, which has been known to fudge the grading on occasion...

but i feel much better about it if you think my approach looked good, thanks for all the help :)