Answer:
a) [tex]\alpha = 18.75\,\frac{rad}{s^{2}}[/tex], b) [tex]n \approx 14920.776\,rev[/tex]
Explanation:
a) The final angular speed is:
[tex]\omega = \frac{v}{R}[/tex]
[tex]\omega = \frac{150\,\frac{m}{s} }{0.08\,m}[/tex]
[tex]\omega = 1875\,\frac{rad}{s}[/tex]
The angular acceleration experimented by the centrifuge is determined by means of the following kinematic expression:
[tex]\alpha = \frac{\omega - \omega_{o}}{\Delta t}[/tex]
[tex]\alpha = \frac{1875\,\frac{rad}{s} - 0\,\frac{rad}{s} }{100\,s}[/tex]
[tex]\alpha = 18.75\,\frac{rad}{s^{2}}[/tex]
b) The change in angular position is:
[tex]\Delta \theta = \frac{\omega^{2}-\omega_{o}^{2}}{2\cdot \alpha}[/tex]
[tex]\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)}[/tex]
[tex]\Delta \theta = 93750\,rad[/tex]
Lastly, the total amount of revolutions made by the centrifuge is:
[tex]n = (93750\,rad)\cdot \left(\frac{1}{2\pi}\,\frac{rev}{rad} \right)[/tex]
[tex]n \approx 14920.776\,rev[/tex]
