Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 8 - Dynamics II: Motion in a Plane - Exercises and Problems: 22

Answer

The minimum angular velocity is 29.9 rpm.

Work Step by Step

We can find the minimum angular velocity at the top of the circle. At the minimum angular velocity, the force of gravity provides the centripetal force to keep the water moving in a circle. We can let the radius of rotation be 1.0 meter. $F_c = m~\omega^2 ~r = mg$ $\omega = \sqrt{\frac{g}{r}}$ $\omega = \sqrt{\frac{9.80~m/s^2}{1.0~m}}$ $\omega = 3.13~rad/s$ We can convert the minimum angular velocity to rpm. $\omega = (3.13~rad/s)(\frac{1~rev}{2\pi~rad})(\frac{60~s}{1~min})$ $\omega = 29.9~rpm$ The minimum angular velocity is 29.9 rpm
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