Question

the earth rotates about its axis once every 23 hours, 56 minutes and 4 seconds. Approximate the number of radians the earth rotates in one second.

Answer 1

Answer:

$\frac{\pi}{43082}\text{ radians per second}$

Step-by-step explanation:

Given,

Time taken in one rotation of earth = 23 hours, 56 minutes and 4 seconds.

Since, 1 minute = 60 seconds and 1 hour = 3600 seconds,

⇒ Time taken in one rotation of earth = (23 × 3600 + 56 × 60 + 4) seconds

= 86164  seconds,

Now,  the number of radians in one rotation = 2π,

That is, 86164 seconds = 2π radians

$\implies 1\text{ second }=\frac{2\pi}{86164}=\frac{\pi}{43082}\text{ radians}$

Hence, the number of radians in one second is $\frac{\pi}{43082}$