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)