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A.2 Orbital Motion a. An object moves under a central force F(r) = -k/p”. The radial component of Newton's Second Law in
Posted: Mon May 09, 2022 5:47 pm
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- A 2 Orbital Motion A An Object Moves Under A Central Force F R K P The Radial Component Of Newton S Second Law In 1 (88.82 KiB) Viewed 23 times
A.2 Orbital Motion a. An object moves under a central force F(r) = -k/p”. The radial component of Newton's Second Law in polar coordinates can be written as dr dt2 F(r) + L2 m m2r3 Substituting u = 1/r and changing the independent variable to 0, show that = du kmun-2 - U. L2 do2 b. Argue that for F(r) = -k/m3, the motion is that of a simple harmonic oscillator in u(0), and determine its frequency. c. Starting from the velocity V expressed in polar coordinates, show that (for any central force) the kinetic energy T = žmū. in polar coordinates can be written as 2 dr 1 1 T= m 2 dt +3mr_w?. 2 Using this, determine the total energy of an object moving under the force F(r) = -k/93.