A 2 Orbital Motion A An Object Moves Under A Central Force F R K R The Radial Component Of Newton S Second Law In 1 (41.29 KiB) Viewed 22 times
A 2 Orbital Motion A An Object Moves Under A Central Force F R K R The Radial Component Of Newton S Second Law In 2 (41.29 KiB) Viewed 22 times
A 2 Orbital Motion A An Object Moves Under A Central Force F R K R The Radial Component Of Newton S Second Law In 3 (41.29 KiB) Viewed 22 times
A 2 Orbital Motion A An Object Moves Under A Central Force F R K R The Radial Component Of Newton S Second Law In 4 (41.29 KiB) Viewed 22 times
A.2 Orbital Motion a. An object moves under a central force F(r) = -k/r". The radial component of Newton's Second Law in polar coordinates can be written as 12 m Substituting u = 1/r and changing the independent variable to 6, show that u. d02 [5] [5] b. Argue that for F(r) = -k/r, 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 = {mývin polar coordinates can be written as T-m dr de + žmriwa [5] Using this, determine the total energy of an object moving under the force F(r) = -k/ d. Show that the effective potential, defined as the components of the energy that depend only on r, is proportional to 1/2. Furthermore, show that for L = km, the effective potential is identically zero. e. For L = km, show that the frequency of oscillation from part (b) vanishes. Write down the total energy in this case, and describe in words what the motion must look like [5] [5]
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