Solution Found!
Imagine that this world is perfectly rigid, uniform, and
Chapter 10, Problem 10.47(choose chapter or problem)
Imagine that this world is perfectly rigid, uniform, and spherical and is spinning about its usual axis at its usual rate. A huge mountain of mass 10-8 earth masses is now added at colatitude 60, causing the earth to begin the free precession described in Section 10.8. How long will it take the North Pole (defined as the northern end of the diameter along co) to move 100 miles from its current position? [Take the earth's radius to be 4000 miles.]
Questions & Answers
QUESTION:
Imagine that this world is perfectly rigid, uniform, and spherical and is spinning about its usual axis at its usual rate. A huge mountain of mass 10-8 earth masses is now added at colatitude 60, causing the earth to begin the free precession described in Section 10.8. How long will it take the North Pole (defined as the northern end of the diameter along co) to move 100 miles from its current position? [Take the earth's radius to be 4000 miles.]
ANSWER:Step 1 of 4
Once the mountain has been added, the earth has only one axis of symmetry \(e_{3}\), which goes through the mountain. ln accordance with (10.93), the angular velocity \(\omega\) now precesses about the mountain at a rate \(\Omega_{\mathrm{b}}\) (as seen by us on earth), where (if \(M\) denotes the mass of the earth and \(m = 10^{-8}M\) that of the mountain)