# The axis of Earth makes a 23.5° angle with a direction

## Problem 48PE Chapter 10

Physics: Principles with Applications | 6th Edition

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Physics: Principles with Applications | 6th Edition

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Problem 48PE

The axis of Earth makes a 23.5° angle with a direction perpendicular to the plane of Earth’s orbit. As shown in Figure 10.41, this axis precesses, making one complete rotation in 25,780 y. (a) Calculate the change in angular momentum in half this time. (b) What is the average torque producing this change in angular momentum? (c) If this torque were created by a single force (it is not) acting at the most effective point on the equator, what would its magnitude be?

Step-by-Step Solution:

Step-by-step solution Step 1 of 9 The change in angular momentum in half its time is calculated as, Here is the angular momentum of the earth about its axis, is the moment of inertia of the Earth and is the angular velocity of the axis. Step 2 of 9 (a) Refers to the figure 10.41 provided in the textbook. The formula to find the change in momentum is, Here is the change in angular momentum. Step 3 of 9 Substitute for , Therefor e, the change in angular momentum is . Step 4 of 9 (b) Convert the time in second, Step 5 of 9 Therefore, the change in time is,

Step 6 of 9

Step 7 of 9

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