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

Question

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.

Answer 1

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)