Answer to Question #27530 in Mechanics | Relativity for hem raj

Question #27530
Express the rotational kinetic energy of the earth in terms of its period of rotation. The moment of inertia of the earth about its spin axis is 8.04 × 1037 kg m2. Calculate its rotational kinetic energy.
1
Expert's answer
2013-04-04T05:03:12-0400
The formula for kinetic energy is:
E=wJ^2/2

where J is the moment of inertia of the Earth about its spin axis,
and w is its angular velocity.
Angular velocity is related to period of rotation as
w=2pi/T = 2 pi/ (24 hours) = 2 pi/(86400 seconds)

The energy is
E =& 2 pi/(86400 seconds) *& 8.04 × 10^(37) kg m^2 = 58.5 J × 10^(32)

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