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Answer:
a)
, b) ![n \approx 14920.776\,rev](https://tex.z-dn.net/?f=n%20%5Capprox%2014920.776%5C%2Crev)
Explanation:
a) The final angular speed is:
![\omega = \frac{v}{R}](https://tex.z-dn.net/?f=%5Comega%20%3D%20%5Cfrac%7Bv%7D%7BR%7D)
![\omega = \frac{150\,\frac{m}{s} }{0.08\,m}](https://tex.z-dn.net/?f=%5Comega%20%3D%20%5Cfrac%7B150%5C%2C%5Cfrac%7Bm%7D%7Bs%7D%20%7D%7B0.08%5C%2Cm%7D)
![\omega = 1875\,\frac{rad}{s}](https://tex.z-dn.net/?f=%5Comega%20%3D%201875%5C%2C%5Cfrac%7Brad%7D%7Bs%7D)
The angular acceleration experimented by the centrifuge is determined by means of the following kinematic expression:
![\alpha = \frac{\omega - \omega_{o}}{\Delta t}](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%5Cfrac%7B%5Comega%20-%20%5Comega_%7Bo%7D%7D%7B%5CDelta%20t%7D)
![\alpha = \frac{1875\,\frac{rad}{s} - 0\,\frac{rad}{s} }{100\,s}](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%5Cfrac%7B1875%5C%2C%5Cfrac%7Brad%7D%7Bs%7D%20-%200%5C%2C%5Cfrac%7Brad%7D%7Bs%7D%20%7D%7B100%5C%2Cs%7D)
![\alpha = 18.75\,\frac{rad}{s^{2}}](https://tex.z-dn.net/?f=%5Calpha%20%3D%2018.75%5C%2C%5Cfrac%7Brad%7D%7Bs%5E%7B2%7D%7D)
b) The change in angular position is:
![\Delta \theta = \frac{\omega^{2}-\omega_{o}^{2}}{2\cdot \alpha}](https://tex.z-dn.net/?f=%5CDelta%20%5Ctheta%20%3D%20%5Cfrac%7B%5Comega%5E%7B2%7D-%5Comega_%7Bo%7D%5E%7B2%7D%7D%7B2%5Ccdot%20%5Calpha%7D)
![\Delta \theta = \frac{\left(1875\,\frac{rad}{s} \right)^{2}-\left(0\,\frac{rad}{s} \right)^{2}}{2\cdot \left(18.75\,\frac{rad}{s^{2}} \right)}](https://tex.z-dn.net/?f=%5CDelta%20%5Ctheta%20%3D%20%5Cfrac%7B%5Cleft%281875%5C%2C%5Cfrac%7Brad%7D%7Bs%7D%20%5Cright%29%5E%7B2%7D-%5Cleft%280%5C%2C%5Cfrac%7Brad%7D%7Bs%7D%20%5Cright%29%5E%7B2%7D%7D%7B2%5Ccdot%20%5Cleft%2818.75%5C%2C%5Cfrac%7Brad%7D%7Bs%5E%7B2%7D%7D%20%5Cright%29%7D)
![\Delta \theta = 93750\,rad](https://tex.z-dn.net/?f=%5CDelta%20%5Ctheta%20%3D%2093750%5C%2Crad)
Lastly, the total amount of revolutions made by the centrifuge is:
![n = (93750\,rad)\cdot \left(\frac{1}{2\pi}\,\frac{rev}{rad} \right)](https://tex.z-dn.net/?f=n%20%3D%20%2893750%5C%2Crad%29%5Ccdot%20%5Cleft%28%5Cfrac%7B1%7D%7B2%5Cpi%7D%5C%2C%5Cfrac%7Brev%7D%7Brad%7D%20%20%5Cright%29)
![n \approx 14920.776\,rev](https://tex.z-dn.net/?f=n%20%5Capprox%2014920.776%5C%2Crev)
The total energy produced by the generator is 3.45 kJ. Of this energy, 2.23 kJ are lost because friction and electrical resistance, so this amount of energy is converted into thermal energy. This means that the rest of the energy is available as electric energy, and it is equal to: