Universe: Stars And Galaxies
6th Edition
ISBN: 9781319115098
Author: Roger Freedman, Robert Geller, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 26, Problem 32Q
To determine
The reason for the astronomers to suspect the structures having the size of globular clusters to be the ones among the first objects that were formed in the history of the universe and not something that are larger.
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A planar double pendulum consists of two point masses \[m_1 = 1.00~\mathrm{kg}, \qquad m_2 = 1.00~\mathrm{kg}\]connected by massless, rigid rods of lengths \[L_1 = 1.00~\mathrm{m}, \qquad L_2 = 1.20~\mathrm{m}.\]The upper rod is hinged to a fixed pivot; gravity acts vertically downward with\[g = 9.81~\mathrm{m\,s^{-2}}.\]Define the generalized coordinates \(\theta_1,\theta_2\) as the angles each rod makes with thedownward vertical (positive anticlockwise, measured in radians unless stated otherwise).At \(t=0\) the system is released from rest with \[\theta_1(0)=120^{\circ}, \qquad\theta_2(0)=-10^{\circ}, \qquad\dot{\theta}_1(0)=\dot{\theta}_2(0)=0 .\]Using the exact nonlinear equations of motion (no small-angle or planar-pendulumapproximations) and assuming the rods never stretch or slip, determine the angle\(\theta_2\) at the instant\[t = 10.0~\mathrm{s}.\]Give the result in degrees, in the interval \((-180^{\circ},180^{\circ}]\).
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Chapter 26 Solutions
Universe: Stars And Galaxies
Ch. 26 - Prob. 1QCh. 26 - Prob. 2QCh. 26 - Prob. 3QCh. 26 - Prob. 4QCh. 26 - Prob. 5QCh. 26 - Prob. 6QCh. 26 - Prob. 7QCh. 26 - Prob. 8QCh. 26 - Prob. 9QCh. 26 - Prob. 10Q
Ch. 26 - Prob. 11QCh. 26 - Prob. 12QCh. 26 - Prob. 13QCh. 26 - Prob. 14QCh. 26 - Prob. 15QCh. 26 - Prob. 16QCh. 26 - Prob. 17QCh. 26 - Prob. 18QCh. 26 - Prob. 19QCh. 26 - Prob. 20QCh. 26 - Prob. 21QCh. 26 - Prob. 22QCh. 26 - Prob. 23QCh. 26 - Prob. 24QCh. 26 - Prob. 25QCh. 26 - Prob. 26QCh. 26 - Prob. 27QCh. 26 - Prob. 28QCh. 26 - Prob. 29QCh. 26 - Prob. 30QCh. 26 - Prob. 31QCh. 26 - Prob. 32QCh. 26 - Prob. 33QCh. 26 - Prob. 34QCh. 26 - Prob. 35QCh. 26 - Prob. 36QCh. 26 - Prob. 37QCh. 26 - Prob. 38QCh. 26 - Prob. 39QCh. 26 - Prob. 40QCh. 26 - Prob. 41QCh. 26 - Prob. 42QCh. 26 - Prob. 43QCh. 26 - Prob. 44QCh. 26 - Prob. 45QCh. 26 - Prob. 46QCh. 26 - Prob. 47Q
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