Calculate the kinetic energy that the earth has because of (a) its rotation about its own axis and (b) its motion around the sun. Assume that the earth is a uniform sphere and that its path around the sun is circular. For comparison, the total energy used in the United States in one year is about 1.1 x 1020 J

To calculate the kinetic energy of the Earth due to its rotation about its own axis, you will need to know the mass (m) of the Earth, and its rotational speed or angular velocity (ω). The formula for rotational kinetic energy is:

Kinetic energy (KE) = 1/2 * I * ω^2

where I is the moment of inertia of the Earth. For a uniform sphere, the moment of inertia is given by:

I = (2/5) * m * r^2

where r is the radius of the Earth. Substituting this into the earlier formula, we get:

KE = 1/2 * (2/5) * m * r^2 * ω^2

To calculate the kinetic energy of the Earth due to its motion around the sun, we need to consider its orbital motion. The formula for the kinetic energy of an object in circular motion is:

KE = 1/2 * m * v^2

where m is the mass of the Earth and v is its orbital velocity around the sun. The orbital velocity can be calculated using the following formula:

v = 2 * π * r / T

where r is the radius of the Earth's orbit and T is the period of its orbit around the sun.

Now, we need to convert the energy consumption in the United States to Joules. 1.1 x 10^20 J represents the total energy used in the United States in one year.

Once you have all the necessary values, plug them into the respective formulas and calculate the kinetic energy due to rotation and orbital motion.