In the diagram, Disk 1 has a moment of inertia of 3.80 kg middot m^2 and is rota

Question

In the diagram, Disk 1 has a moment of inertia of 3.80 kg middot m^2 and is rotating in the counterclockwise direction with an angular speed of 7.30 rad/s about a frictionless rod passing through its center. A second disk rotating clockwise with an angular speed of 9.30 rad/s falls from above onto Disk 1. The two then rotate as one in the clockwise direction with an angular speed of 2.80 rad/s. Determine the moment of inertia of Disk 2. Review sign conventions for angular velocity. Consider conservation of angular momentum, kg middot m^2

Explanation / Answer

conservation of angular momentum
I1w1+I2w2=Iw
where
I=I1+I2
then
I1w1+I2w2=I1w+I2w
I2=I1(w1-w)/(w-w2)
where

w1 = 7.3 rad/s

w2 = -9.3 rad/s

w = -2.8 rad/s

i1 = 3.8 kg-m^2

I2 = 3.8(7.3+2.8)/(-2.8+9.3) = 5.9 kg.m^2

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