Question

Calculate the translational kinetic energy of Earth as it orbits the Sun once each year (the Earth

Answer 1

the translational kinetic energy of the earth is given as ::

K.E_{translational} = 1/2 m v²                                { eq.1 }

where, m = mass of the earth = 5.98 x 10²⁴ kg

v = r

inserting the value of 'v' in above eq.

K.E_{translational} = 1/2 m (r )²

K.E_{translational} = 1/2 m r²²                       { eq.2 }

the rotational kinetic energy of the earth is given as ::

K.E_rotational = 1/2 I ²                        { eq.3 }

where, I = moment of inertia of solid sphere = (2 / 5) m r²

= angular velocity

inserting the values of 'I' in eq.3,

K.E_rotational = (1/5) m r²²                          { eq.4 }

Comparing the translational kinetic energy to the rotational kinetic energy which is given as ::

from eq. 2 & 4,

K.E_{translational} / K.E_rotational = (1/2) m r²² / (1/5) m r²²

K_tr / K_rot = (1 / 2) x (5 / 1)

K_tr / K_rot = 5 / 2