Final answer:
The total mechanical energy associated with Earth's rotational motion is the sum of the rotational kinetic energy of Earth on its axis and the rotational kinetic energy of Earth in its orbit around the Sun.
Step-by-step explanation:
The total mechanical energy associated with Earth's rotational motion can be calculated by summing the rotational kinetic energy of Earth on its axis and the rotational kinetic energy of Earth in its orbit around the Sun.
a) To calculate the rotational kinetic energy of Earth on its axis, we use the formula:
K = (1/2) * I * ω2
where K is the kinetic energy, I is the moment of inertia, and ω is the angular velocity. The moment of inertia of a solid sphere is given by I = (2/5) * M * R2, where M is the mass and R is the radius of the sphere.
b) To calculate the rotational kinetic energy of Earth in its orbit around the Sun, we use the same formula as in part a, but with a different moment of inertia. The moment of inertia for a point mass revolving around an axis is given by I = M * R2, where M is the mass and R is the distance from the axis of rotation.