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Notes 2 for June 18 prepared by Melanie Smith Shusaku discussed
Notes 2 for June 18 prepared by Melanie Smith Shusaku discussed

... E = F/q     and E = K(Q/r2) F = qE If F is constant, E is constant, and since F = ma, the proton will move at a constant rate. We skipped going over this problem, as we have not gotten to it in the lecture notes yet. Electrical force and gravitational forces are two non-contact forces. In considerin ...
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... Newton’s laws still apply to every mass element of the extended body, so there is motion, momentum, work, energy (potential and kinetic), etc. associated to the motions about the center of mass of the body. For a rigid body, that motion takes the form of rotations. Relaxing the rigidity assumption, ...
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... For which values of ρ0 and R would you expect a black hole to be implied? (Hint: Escape speed?) Given that Newtonian gravity is fully described by the Poisson equation ∇ 2 Φ = 4π G ρ (x), formally derive the acceleration −∇Φ for this mass distribution using the divergence theorem. What is the veloci ...
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Classical central-force problem



In classical mechanics, the central-force problem is to determine the motion of a particle under the influence of a single central force. A central force is a force that points from the particle directly towards (or directly away from) a fixed point in space, the center, and whose magnitude only depends on the distance of the object to the center. In many important cases, the problem can be solved analytically, i.e., in terms of well-studied functions such as trigonometric functions.The solution of this problem is important to classical physics, since many naturally occurring forces are central. Examples include gravity and electromagnetism as described by Newton's law of universal gravitation and Coulomb's law, respectively. The problem is also important because some more complicated problems in classical physics (such as the two-body problem with forces along the line connecting the two bodies) can be reduced to a central-force problem. Finally, the solution to the central-force problem often makes a good initial approximation of the true motion, as in calculating the motion of the planets in the Solar System.
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