GRE study help-classical physics

[lifes3ps]

last problem with classical- thermo last night was a breeze.

problem:
child on edge of solid disk (merry goround)
M(child)=40kg
M(disk)=200kg
r(disk)=2.5m
w(disk)=2.0rad/s

child moves to center, whats final angular velocity of merry go round?, neglecting size of child.

my work:
here i add the mass of the child and disk for I=kmr^2.
K=0.5 for disk, thus I=(1/2)*(240)*(2.5)^2=750.

L=Iw=750*2=1500.

conserving L, changing I
I'=1/2*200*2.5^2=625
L'=I'w', 1500=625*w' -> w'=2.4 [rad/s]. which is not the answer

correct: 2.8 [rad/s], where am i going wrong?

**note, if i didnt say above, child starts on edge of disk, @r=2.5m

[daryn]

just a quick glance, your I' looks right since the child is at the center and doesn't add to the rotational inertia

however when you initially calculated I it looks like you just calculated it as if the disk itself was 240 kg total, but it makes a difference that the child is on the end not near the center.

[daryn]

the initial moment of inertia I should be Idisk + Ichild

Idisk = .5*200*2.5^2 = 625

Ichild = 40*2.5^2 = 250

so I = 875

I' = 625

L = Iw = 875*2 = 1750

L' = I'w' = 625*w' = 1750

w' = 1750/625 = 2.8 rad/s

[Schweitzer]

To restate, when combining moments of inertia you need to add the seperate moments of inertia and account for the displacement from the rotation axis.

I= I(disk) + I(child) + m(child)*r^2

where r is the displacement of the child from the axis it is rotating around.
(In this problem it asks to ignore the size of the child, thus you assume the child is a point particle with no moment of inertia so you only need the displacement term)