Part A A particle of mass m with angular momentum L is moving in a central force potential U(r) = -kr-a where a = 1.5 an

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Part A A Particle Of Mass M With Angular Momentum L Is Moving In A Central Force Potential U R Kr A Where A 1 5 An 1 (28.71 KiB) Viewed 17 times

Part A A particle of mass m with angular momentum L is moving in a central force potential U(r) = -kr-a where a = 1.5 and k is a positive real number. a. Make a sketch showing U(r), the centrifugal potential energy Uc(r), and the effective potential Ver(r). b. Find r, the radius of a circular orbit in this effective potential. (Remember, in a circular orbit U(ro) = constant. Consequently T = E - U will also be constant). C. Show that for this circular orbit T = d. By making a Taylor expansion of Vertr) about ro, show that the find Wosc, the frequency of small oscillations about the circular orbit if the particles are disturbed from the separation ro.