Answer
a) The length of the arm of the centrifuge is $5.02m$
b) The angular acceleration of the centrifuge is $7rad/s^2$
Work Step by Step
a) In the first exercise, $\omega=2.5rad/s$ and $a_c=3.2\times9.8m/s^2=31.36m/s^2$
The length of the arm of the centrifuge is $$a_c=r\omega^2$$ $$r=\frac{a_c}{\omega^2}=5.02m$$
b) In the second exercise, the total acceleration $a=4.8\times9.8m/s^2$. Total acceleration is comprised of centripetal and tangential accelerations, so $$a_T^2=a^2-a_c^2=(9.8m/s^2)^2(4.8^2-3.2^2)=1229.312$$ $$a_T=35.06m/s^2$$
The angular acceleration of the centrifuge is $$\alpha=\frac{a_T}{r}=7rad/s^2$$
