Theoretical Mechanics for Sixth Forms

PrefaceChapter I. Introduction. The Fundamental Concepts of Theoretical Mechanics 1.1. The Nature of Theoretical Mechanics 1.2. Newton's Axioms 1.3. The Unit of Mass and the Unit of Force 1.4. Gravitational Units of ForceChapter II. Systems of Coplanar Forces Acting on a Particle 2.1. Vector Quantities 2.2. Velocities and Accelerations as Vectors 2.3. Force as a Vector 2.4. The Parallelogram of Forces 2.5. Equilibrium of Forces 2.6. Forces in the Physical World 2.7. The Resultant of Any Number of Forces Acting on a Particle 2.8. The Equilibrium of a Rigid Body Acted Upon by Three Forces Only 2.9. Two Useful Trigonometric Formula 2.10. Elastic Strings 2.11. Particles Suspended from a StringChapter III. The Kinematics of a Particle Moving in a Straight Line 3.1. Relationships between Distance, Time, Velocity and Acceleration 3.2. Graphical Relationships 3.3. Uniformly Accelerated Motion in a Straight Line 3.4. Free Motion under GravityChapter IV. Projectiles 4.1. The Resolution of Uniplanar Motion into Components at Right Angles 4.2. The Free Motion of a Projectile 4.3. The Equation of the Path 4.4. The Parabolic Path of a Projectile 4.5. The Range on an Inclined PlaneChapter V. Relative Motion 5.1. Relative Position 5.2. Relative Velocity 5.3. Problems of Relative Position and InterceptionChapter VI. The Moment of a Force 6.1. The Law of the Lever 6.2 The Resultant of a System of Parallel Forces 6.3 Equilibrium of a Rigid Body Acted Upon by a System of Coplanar Forces 6.4 Graphical Representation of the Moment of a ForceChapter VII. Centers of Gravity 7.1. Definition 7.2. The Center of Gravity of a Finite Number of Coplanar Particles 7.3. The Center of Gravity of a Rigid Body 7.4. The Center of Gravity of a Compound Body 7.5. The Position of a Freely Suspended Body 7.6. The Equilibrium of a Body at Rest on a Horizontal Plane 7.7. The Centers of Gravity of Some Common SolidsChapter VIII. The Dynamics of a Particle 8.1. Newton's Laws of Motion 8.2. The Motion of Connected Particles 8.3. Impulse and Momentum 8.4. Conservation of Momentum 8.5. Work and EnergyChapter IX. Friction 9.1. The Nature of Friction 9.2. The Laws of Friction 9.3. The Angle of Friction 9.4. The Equilibrium of a Particle on an Inclined Plane 9.5. Examples Involving FrictionChapter X. Conservation of Energy 10.1. Energy in the Physical World 10.2. Conservation of Mechanical Energy 10.3. The Relation between the Energy Equation and the Equation of MotionChapter XI. The Impact of Elastic Bodies 11.1. Direct Collision of Elastic Spheres 11.2. Impulsive Reaction and Loss of Kinetic Energy 11.3. The Collision between a Smooth Sphere and a Fixed Smooth Plane 11.4. Oblique Impact of Smooth Elastic SpheresChapter XII. Power 12.1. Definition and Units 12.2. Power with a Constant Force 12.3. Energy and Power 12.4. The Acceleration and the Maximum Speed of a CarChapter XIII. Motion in a Circle 13.1. The Motion of a Particle Which is Not Moving in a Straight Line 13.2. Angular Velocity and Angular Acceleration 13.3. Uniform Speed in a Circle 13.4. Some Examples of Uniform Circular Motion in a Horizontal Circle 13.5. Motion in a Circle When the Speed is Not Necessarily Uniform 13.6. Motion in a Vertical CircleChapter XIV. Simple Harmonic Motion 14.1. Some Oscillatory Motions 14.2. The Solution of the Equation of SHM 14.3. Two Particular Integrals of the SHM Equation 14.4. The Projection of Uniform Motion in a Circle on to a Diameter 14.5. The Motion of a Particle Attached to a Light Elastic Spring 14.6. The Motion of a Particle Attached to Two Elastic Strings 14.7. Problems Involving the Equation of Motion ẍ=-ω2x+c 14.8. The Motion of the Center of Mass of Two Moving Particles 14.9. The Rectilinear Motion in a Horizontal Plane of Two Particles Which are Connected by an Elastic Spring 14.10. Small OscillationsAnswers To the ExercisesIndex