Question

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?

Chapter 11, Problem 055 Your answer is partially correct. 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? Une Number2.559 the tolerance is +/-2% Click if you would like to Show Work for this question: Units T rad/s Open Show Work

Answer 1

answer) by applying conservation of angular moment we have

initial momentum= final momentum

I$\omega$i=(I+I1) $\omega$f

I1= inertia of putty=mr²

so we have

I$\omega$i=(I+mr²)$\omega$f

so $\omega$f=I$\omega$i/I+mr²

now putting the values we get

$\omega$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