Answer to Question #174451 in Classical Mechanics for Rohan

Question

In one second the earth rotates about its axis by an angle θ where

(a) θ < 10^-6  radian

(b) 10^-6 radian< θ< 10^-5 radian

(c) 10^-5 radian < θ < 10^-4 radian

(d) θ > 10^-4 radian

Answer 1

Let's first find the angular speed of Earth's rotation about its axis:

$$\omega=\dfrac{\Delta \theta}{\Delta t},$$ $$\omega=\dfrac{2\pi\ rad}{1\ d}\cdot\dfrac{1\ d}{24\ h\cdot3600\ \dfrac{s}{1\ h}}=7.27\cdot10^{-5}\ \dfrac{rad}{s}.$$

Then, in one second the Earth rotates about its axis by an angle $\theta$ equals:

$$\theta=\omega t,$$ $$\theta=7.27\cdot10^{-5}\ \dfrac{rad}{s}\cdot1\ s=7.27\cdot10^{-5}\ rad.$$

Therefore, the correct answer is (c).

Answer:

(c) 10^-5 radian < θ < 10^-4 radian.