# 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.

of inertia of the earth about its spin axis is 8.04 × 1037 kg m2. Calculate its rotational kinetic

energy.

Expert's answer

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)

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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