# Angular speed of multi-particle system

1. Nov 14, 2009

### luvlybug1025

1. The problem statement, all variables and given/known data

A small mouse of mass 50 g drops straight down upon and grabs onto the outer edge of
a freely rotating disk of initial speed of 30 rev/min. The moment of inertia of the disk is
0.005 kg-m2 and its radius is 20 cm.
a) Find the angular speed of the disk after the mouse gets attached to it.
b) The mouse now scrambles to the center of the disk. Find the angular speed of
the system after it gets there.

2. Relevant equations

L=Iw
v=rw

3. The attempt at a solution

If L=Iw, then L=mrv and w=L/I

w=(mrv)/(Isystem)=(mrv)/(Idisk + I mouse)

Idisk = .005kg*m^2, so mdisk = 0.25kg

Now, w = (0.30kg)(0.20m)(v) / (0.005kg*m^2 + 0.002kg*m^2)

If v=rw and I convert w=30rev/min to rad/s, then v= 0.63 rad*m/s

Then, my final w = 5.4 rad/s

The original was 3.14 rad/s. Shouldn't the disk slow down when the mouse drops on it? The moment of inertia of the system dropped. I think I may be missing something when converting units because it doesn't make sense to me. If I get this part, then I think I can handle part b on my own.

Last edited: Nov 14, 2009
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