# Chapter 8 - Dynamics II: Motion in a Plane - Exercises and Problems - Page 211: 7

The number of revolutions that the electron makes per second is $6.6\times 10^{15}~rev/s$

#### Work Step by Step

The centripetal force is the net force which keeps an object moving in a circle. In this case, the electric force provides the centripetal force to keep the electron moving in a circle. We can find the speed of the electron. $F = \frac{mv^2}{r}$ $v^2 = \frac{F~r}{m}$ $v = \sqrt{\frac{F~r}{m}}$ $v = \sqrt{\frac{(8.2\times 10^{-8}~N)(5.3\times 10^{-11}~m)}{9.1\times 10^{-31}~kg}}$ $v = 2.185\times 10^6~m/s$ We can use the speed to find the number of revolutions per second. Let $N$ be the number of revolutions per second. $N = (v)(\frac{1~rev}{2\pi ~r})$ $N = (2.185\times 10^6~m/s)(\frac{1~rev}{(2\pi)(5.3\times 10^{-11}~m)})$ $N = 6.6\times 10^{15}~rev/s$ The number of revolutions that the electron makes per second is $6.6\times 10^{15}~rev/s$

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