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A horizontal disc rotating freely about a vertical axis makes 100rpm.A small piece of wax of mass 10kg falls vertically on the disc and adheres to it at a distance of 9cm from the axis.If the number of revolutions per minute is thereby reduced to 90.Calculate the moment of inertia of disc.
taking wax & disk as a system ....
then there is no external torque acting on this system so angular momentam will remain conserved..
IW = IfWf ..............1
finally moment of inertia = I + Iwax
Iwax = mr2 = 10(9*10-2)2 (r = 9cm = 9*10-2m & m =10kg )
= 0.081 kg-m2
If = I + 0.081 ..........2
putting 2 in 1
IW = (I+0.081)Wf
W/Wf = (1+.081/I) {W = 100rpm & Wf=90rpm (given)}
100/90 = 1 + 0.081/I
I = 0.729kg-m2
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