A horizontal vinyl record of mass 0.0856 kg and radius 0.0898 m rotates freely about a vertical axis through its center with an angular speed of 5.82 rad/s and a rotational inertia of 5.42 x 10-4 kg·m2. Putty of mass 0.0267 kg drops vertically onto the record from above and sticks to the edge of the record.What is the angular speed of the record immediately afterwards?
answer) by applying conservation of angular moment we have
initial momentum= final momentum
Ii=(I+I1) f
I1= inertia of putty=mr2
so we have
Ii=(I+mr2)f
so f=Ii/I+mr2
now putting the values we get
f=5.42*10-4*5.82/5.42*10-4+(0.0267*0.08982)=4.17 rad/s
so the answer is 4.17 rad/s or 4.2 rad/s or 4.165 rad/s
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