CENTRAL - FORCE MOTION A. REDUCED MASS B. CONSERVATION THEOREMS C. EQUATIONS OF MOTION Marilyn P. Mifuel Student, WVSU Ph D Science Education (Physical Science) May 1of 2020 WHAT IS A CENTRAL FORCE? • FORCE… * always acts TOWARD or AWAY (radially pointing), from a fixed point and… * * magnitude depends ONLY on DISTANCE from the point WHAT IS CENTRAL FORCE MOTION? • Motion of a system consisting of two bodies affected by a force directed along the line connecting the centers of the two bodies EXAMPLES…AND APPLICATIONS… A. GRAVITAIONAL FORCE - Motion of celestial bodies (planets, moons, comets, etc.) - B. ELECTROSTATIC FORCE -two-body nuclear interaction (scattering of alpha particles by a nuclei); electrons revolve around the nucleus C. SPRING FORCE- simple harmonic motion WHY IS CENTRAL FORCE A CONSERVATIVE FORCE? F (r) = - dU dr Where F(r) magnitude of central force U(r) time- independent potential energy THEOREMS THAT RELATE CENTRAL FORCE WITH ANGULAR MOMENTUM • 1. For an object to have its angular momentum conserved, the object should be subjected ONLY to Central Force • 2. For an object to have its motion on a plane, the object should be subjected ONLY to Central Force SPECIAL CLASS OF PROPERTIES ASSOCIATED WITH MOTION OF PARTICLES IN A CENTRAL FORCE FIELD • 1. By nature, Central Force is a conservative field; Hence E= constant (scalar) • 2. If a particle is moving in a central force field and NO other forces acting on the particle at the time of motion, the ANGULAR MOMENTUM is conserved. L= constant (vector)- magnitude and direction in space is constant; absence of torque =0 • 3. Motion is PLANAR- confined to plane polar coordinates A. REDUCED MASS NOTA BENE: Slide no. 9 CONSERVATION THEOREMS: FIRST INTEGRALS OF MOTION EQUATIONS OF MOTION PROBLEM 8.1 FINAL ANSWER FOR 8.1 PROBLEM 8.2 FINAL ANSWER FOR PROBLEM 8.2 REFERENCES Classical Dynamics of Particles and Systems Marion & Thornton, 5th Edition Lecture Notes on Classical Mechanics for Physics 106ab Sunil Golwala, January 15, 2007 • https://physicscatalyst.com/graduation/central-forces/ • https://byjus.com/physics/central-force/
