Physics (10th Edition)

Published by Wiley

Chapter 8 - Rotational Kinematics - Problems - Page 216: 70

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 $$\alpha=\frac{a_T}{r}=7rad/s^2$$

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