Kinetic energy?

Question

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 9.33 109 J

(a) Calculate the kinetic energy that the earth has because of its rotation about its own axis.

J

(b) Calculate the kinetic energy that the earth has because of its motion around the sun.

J

Answer 1

The circumference of the Earth's orbit is about 9.40 x 10^11 m

and this distance is covered in 3.16 x 10^7 seconds

for an average velocity of v = 2.98 x 10^4 m/s.

Translational Kinetic Energy is 1/2 m v^2. Plug in the values.

The rotational angular velocity of the Earth is w = 7.29 x 10^5 radians/second (2 pi radians in 24 hours).

The moment of inertia of the Earth is I = 2/5 m r^2.

The mass of the Earth is about 5.97 x 10^24 kg

The radius of the Earth is about 6.38 x 10^6 m

You know mass and radius; plug them in.

Rotational Kinetic Energy is 1/2 I w^2. Plug in the values.