The center of a long frictionless rod is pivoted at the origin, and the rod is forced to rotate in a VERTICAL plane with constant angular velocity \omega. Write down the Lagrangian for a bead of mass m threaded on the rod, using r as your generalized coordinate, where r, \phi are the polar coordinates of the bead. (Notice that \phi is not an independent variable since it is fixed by the rotation of the rod tobe \phi = \omega * t) Solve Lagrange's equation for r(t). What happens if the bead is initially at rest at the origin? If it is released from any point ro > 0, show that r(t) eventually grows exponentially. Explain your results in terms of the centrifugal force m* \omega ^2 *r. This is an altered version of problem 21 in Chapter 7 from Taylor's Classical Mechanics book.Â
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Physics, 21.06.2019 19:40, tmark45
Ogle–2013–blg–0723 is an exoplanet that is similar to earth in size and proximity to its star. this exoplanet has mass m=4.18×1024kg and radius r=5.66×106m. an astronaut whose weight on earth is w=735n lands on the planet. a. calculate m, the mass of the astronaut. b. calculate gp? , the acceleration due to gravity on the surface of ogle–2013–blg–0723. c. calculate wp? , the weight of the astronaut on the surface of ogle–2013–blg–0723. d. calculate v, the minimum velocity required to put an object into orbit above ogle–2013–blg–0723. e. calculate t, the time required to complete an orbit around ogle–2013–blg–0723.
Answers: 3
Physics, 21.06.2019 21:30, galaxyworld36
Janelle made a hypothesis bout the uneven temperatures inside her house during winter. she believes that 50% of the ducts are blocked and she plans to investigate. if she wants to prove her hypothesis using scientific processes what should she do next?
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Physics, 22.06.2019 04:40, hannah1072
How is the gravitational force related to the distance between two objects?
Answers: 1
The center of a long frictionless rod is pivoted at the origin, and the rod is forced to rotate in a...
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