Question

Earth rotates on its axis once every 24 hours.

How long does it take Earth to rotate through an angle of $\frac{\pi }{6}$?

Short answer

The time taken by Earth to rotate through an angle of$\frac{\pi }{6}$ is 2 hours.

Step-by-step solution

Step 1. Given information.

Given, Earth rotates on its axis once every 24 hours.

The time taken by Earth to rotate through an angle of$\frac{\pi }{6}$ is to be determined.

Step 2. Explanation.

Each rotation is $2\pi$ .

Since$2\pi$takes 24 hours, the required time for$\frac{\pi }{6}$ is given by:

$\begin{array}{l}\frac{2\pi }{24}=\frac{\frac{\pi }{6}}{x}\\ \frac{2\pi }{24}=\frac{\pi }{6x}\\ x=2\end{array}$

Step 3. Conclusion.

Hence the time taken by Earth to rotate through an angle of $\frac{\pi }{6}$ is 2 hours.