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Physics: Principles with Applications | 6th Edition | ISBN: 9780321569837 | Authors: Douglas C. Giancoli
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(II) Estimate the kinetic energy of the Earth with respect to the Sun as the sum of two

Chapter 8, Problem 46P

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QUESTION:

Problem 46P

(II) Estimate the kinetic energy of the Earth with respect to the Sun as the sum of two terms, (a) that due to its daily rotation about its axis, and (b) that due to its yearly revolution about the Sun. [Assume the Earth is a uniform sphere with mass 6.0 x 1024 kg, radius = 6.4 x 106 m, and is 1.5 x 108 km from the Sun.]

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QUESTION:

Problem 46P

(II) Estimate the kinetic energy of the Earth with respect to the Sun as the sum of two terms, (a) that due to its daily rotation about its axis, and (b) that due to its yearly revolution about the Sun. [Assume the Earth is a uniform sphere with mass 6.0 x 1024 kg, radius = 6.4 x 106 m, and is 1.5 x 108 km from the Sun.]

ANSWER:

Solution 46P

We are going to find the kinetic energy of the Earth as the sum of the rotational kinetic energy due to its daily rotation and the yearly revolution about the Sun.

Part (a)

Step 1 of 5:

To find the rotational kinetic energy of the Earth about its axis.

The mass of the Earth M = 6 x 1024 kg

The radius of the Earth R = 6.4 x 106 m

The time period of rotation of Earth Td = 8.64 x 104 s

The rotational kinetic energy is expressed as

Where I is the moment of inertia about its axis (for a perfect sphere)

        ⍵d is the angular speed of the rotation of the Earth

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