Intermediate Dynamics

This advanced undergraduate physics textbook presents an accessible treatment of classical mechanics using plain language and clear examples. While comprehensive, the book can be tailored to a one-semester course. An early introduction of the Lagrangian and Hamiltonian formalisms gives students an opportunity to utilize these important techniques in the easily visualized context of classical mechanics. The inclusion of 321 simple in-chapter exercises, 82 worked examples, 550 more challenging end-of-chapter problems, and 65 computational projects reinforce students' understanding of key physical concepts and give instructors freedom to choose from a wide variety of assessment and support materials. This new edition has been reorganized. Numerous sections were rewritten. New problems, a chapter on fluid dynamics, and brief optional studies of advanced topics such as general relativity and orbital mechanics have been incorporated. Online resources include a solutions manual for instructors, lecture slides, and a set of student-oriented video lectures. INTERMEDIATE DYNAMICS Intermediate Dynamics Intermediate Dynamics Second Edition PATRICK HAMILL Organization A One-Semester Course Exercises and Problems Acknowledgments A Brief Review of Introductory Concepts 1.1 Kinematics У Jv = y* aJr. 1.1.1 Motion in a Straight Line at Constant Acceleration Exercise 1.1 1 .2 Newton’s Second Law a = F/m. F = ma. (1.5) 1.3 Work and Energy 1.4 Momentum 1.5 Rotational Motion 1.5.1 Rotational Kinematics 1.5.2 Rotational Dynamics 1.6 Statics 1.7 Rotational Kinetic Energy 1.8 Angular Momentum I = |1| = |r x p| = |rxmv| = rmv sin0, L = £1, = J2(ri x p,). 1.9 Rotational Equivalents N = /a, 1.10 Summary N = r x F. 1 = r x p. 1.11 Problems Computational Projects Kinematics 2.1 Galileo Galilei (Historical Note) 2.2 The Principle of Inertia A body will remain in uniform motion as long as no net external force acts on it. 2.3 Basic Concepts in Kinematics 2.3.1 Motion in One Dimension with Constant Acceleration Exercise 2.1 2.3.2 Projectile Motion 2.3.3 Rotation About a Fixed Axis = -^[(e-c,)(cf+1)-e0(1)] 2.3.4 The Relation between Linear and Rotational Motion vT = (») x r. (2.7) 2.4 The Position of a Particle on a Plane 2.5 Unit Vectors c = a x b a • b = | a | | b | cos(a,b). (2.9) к x i = j, i x к = —j. i J к 2.6 Kinematics in Two Dimensions 2.6.1 Cartesian Coordinates 2.6.2 Plane Polar Coordinates r = r(0), and 2.7 Kinematics in Three Dimensions 2.7.1 Cartesian Coordinates 2.7.2 Cylindrical Coordinates Ф = Ф(0). p • p = 1, ф • ф = 1, к • к = 1, V - Г - £(pp + zk) = pp + + zk. 2.7.3 Spherical Coordinates Ф = Ф(0). Эф . Эф . v = — = — (rr) = —- r + r —, dt dt dt dt 2.8 Summary v = xi + yj + zk, a = xi + yj + zk. r = rr, r = pp + zk, r = rr, 2.9 Problems Army _ 10 Newton’s Laws: Determining the Motion 3.1 Isaac Newton (Historical Note) 3.2 The Law of Inertia A body in motion will remain in uniform motion and a body at rest will remain at rest unless acted upon by a net external force. 3.3 Newtons Second Law and the Equation of Motion The rate of change of the momentum of an isolated body is equal to the net external force applied to it. ^=F, 3.4 Newton s Third Law: Action Equals Reaction To every action there is always opposed an equal reaction.