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Calculate the angular momentum of the spherical earth rotating about its own axis, if the mass of earth =5.98*10^24 kg and mean radius of the earth =6.38*10^6m.

Calculate the angular momentum of the spherical earth rotating about its own axis, if the mass of earth =5.98*10^24 kg and mean radius of the earth =6.38*10^6m.

Grade:

1 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
7 years ago
angular momentum, L
moment of inertia, I
angular velocity = w

L = I w

now in the case of a spherical object the moment of inertia about the line passing through the centre of mass is I = (2/5) * M * R^2
where M = 5.98 * 10^24 kg, is the mass of the body and R = 6.32 * 10^6 m is the radius of the body.

we can work out the angular velocity of the earth since we know the earth take 24 hours to complete a full 2 pi radian rotation

so w = 2 * pi / (24 * 60 * 60 ) radian per second
So from the first equation

L =(( 2/5) * 5.98 * 10^24* (6.32 * 10^6 )^2 * 2 * pi / (24 * 60 * 60 ) )kg meter square per second
Thanks & Regards
Rinkoo Gupta
AskIITians Faculty

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