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July 10th, 2019, 07:15 AM   #1
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How Angular Velocity of Earth is 2π/T?

moment of inertia of the earth; $\displaystyle I = \large \frac {2}{5} \normalsize MR^{2}$

Angular Velocity of Earth ;$\displaystyle ω = \large \frac {2π}{T}$

Here Earth is considered as solid sphere.

I didn't understand how Angular Velocity of Earth is $\displaystyle \large \frac {2π}{T}$?
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July 10th, 2019, 11:59 AM   #2
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Originally Posted by Ganesh Ujwal View Post
moment of inertia of the earth; $\displaystyle I = \large \frac {2}{5} \normalsize MR^{2}$

Angular Velocity of Earth ;$\displaystyle ω = \large \frac {2π}{T}$

Here Earth is considered as solid sphere.

I didn't understand how Angular Velocity of Earth is $\displaystyle \large \frac {2π}{T}$?
It's essentially a definition:
The period of motion is defined as the amount of time for a cycle to be complete. We label this time as T. Then the frequency is defined as $\displaystyle f = \dfrac{1}{T}$ and the angular frequency is $\displaystyle \omega = 2 \pi f = \dfrac{2 \pi}{T}$. this is true for any cyclic system, not just rotation.

-Dan
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