# Chapter 4 - Kinematics in Two Dimensions - Exercises and Problems: 23

The plane's angular velocity with respect to the earth's surface is $7.96^{\circ}/h$

#### Work Step by Step

We can find $f$, the fraction of the earth's circumference that the plane flies: $f = \frac{5000~mi}{2\pi ~4000~mi}$ $f = 0.199$ We can find the angle in degrees that the plane flies with respect to the earth's surface: $\theta = (0.199)(360^{\circ})$ $\theta = 71.64^{\circ}$ We can find the plane's angular velocity with respect to the earth's surface: $\omega = \frac{\Delta \theta}{\Delta t}$ $\omega = \frac{71.64^{\circ}}{9.0~h}$ $\omega = 7.96^{\circ}/h$ The plane's angular velocity with respect to the earth's surface is $7.96^{\circ}/h$.

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