15. [2pt] An empty centrifuge ha rotational inertia of 82000 g cm. It i initiall

Question

15. [2pt] An empty centrifuge ha rotational inertia of 82000 g cm. It i initially holding 4 test tubes, each of which has ma53 of 18 g. Consider the test tubes to be point masse located at a radial position of 14 cm. While the centrifuge is apinning frecly, the contents experience a centripetal acceleration of 55 g'. Then, one of the test tubes breaks, leaking its contents all over the lab floor. Deternine the angular velocity of the centrifuge after the test tube breaka, using units of "rpm' Ansver: Submit AI Answers 16. [2pt] Two arall balls of nas3 2.78 g are attached to the ends of a thin rod of neg11gible as and length 73 em. The rod 13 initially motioniess, but 13 free to rotate without friction about a horizontal axia through its center. A putty wad of maas 120 g drops onto one of the balls, with a speed 2.4 m/s, and sticks to it. hat is the angular speed of the system just after the putty wad hits? putty wad Axis Submit Al Answers 17. [2pt] What is the ratio of the kinetic energy of the entire system after the collision to that of the putty wad before the collision (as a percent)? Do not enter a unit with your answer.) Ansver: Submit Al Answers

Explanation / Answer

here,

rotational inertia , I = 82000 g.cm^2

I = 8.2 * 10^-3 kg.m^2

mass of each test tube , m1 = 0.018 kg

let the velocity be w0

centripital accelration , a = w0^2 * r

55 * 9.81 = w0^2 * 0.14

solving for w0

w0 = 62.1 rad/s

let the final angular speed be w

using conservation of angular momentum

( I + 4 * m * r^2) * w0 = ( I + 3 * m * r^2) * w

( 8.2 * 10^-3 + 4 * 0.018 * 0.14^2) * 62.1 = ( 8.2 * 10^-3 + 3 * 0.018 * 0.14^2) * w

solving for w

w = 64.4 rad/s = 615.2 rpm

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