Elementary Plane Rigid Dynamics

PrefaceChapter One The Motion of a Rigid Body Around a Fixed Axis The Rotation of a Rigid Body around a Fixed Axis The Evaluation of the Moment of Inertia for Some Simple Figures The Moment of Inertia of a Thin Rectangular Plate for a Polar Axis through Its Center of Gravity The Moment of Inertia of a Rectangular Parallelepiped for an Axis Normal to One of Its Faces and through Its Center of Gravity The Moment of Inertia of a Cylinder for an Axis through Its Center of Gravity and Normal to Its Axis of Figure The Moment of Inertia for a Sphere for an Axis through Its Center of Gravity A Note on the Quadratic Moment Problems The Conservation of Angular Momentum The Gyroscope: A Problem in Angular Momentum Rolling Motion Use of the Instantaneous Center A Rolling Body on an Inclined Plane ProblemsChapter Two The General Plane Motion of A Rigid Body The General Plane Motion of a Rigid Body The Meaning of the General Torque Equation for Plane Motion Note on the Inertial Forces Pure Translation The Superelevation of the Outer Rail on a Railway Curve Equilibrium Kinetic Energy ProblemsChapter Three Some Special Problems Involving Friction Belt and Rope Friction Power Transmission by Belts The Efficiency of Belt Transmission. Slip The Friction in a Flat Step Bearing Power Transmitted by a Flat Disk Coupling Rolling Bodies—Limiting Condition for Rolling or Slipping ProblemsChapter Four Undamped Simple Harmonic Motion Definition of Simple Harmonic Motion Definition of SHM Definition of Some Quantities Associated with Vibratory Motion The Quantitative Relations among Velocity, Displacement, and Period in SHM (Undamped) A Mass Vibrating on a Spring The Simple Pendulum The Motion of the Projection on the Diameter of a Point Moving with Uniform Speed on a Circle The Energy of a Body Vibrating with SHM An Alternative Calculation of the Potential Energy The Form of the Expression for the Period of SHM A Useful Expression for the Period in Undamped Harmonic Motion in Terms of the Energy Period for a Mass Hanging on a Heavy Spring Angular Harmonic Motion The Simple Pendulum The Oscillations of a Magnet in a Magnetic Field Comparison of Moments of Inertia Measurement of Rigidity by a Kinetic Method The Bifilar Pendulum The Compound Pendulum Condition for Minimum Period The Center of Percussion ProblemsChapter Five Damped Oscillations Forced Oscillations Free Vibrations with Damping The Logarithmic Decrement—Log dec Energy Forced Oscillations The Amplitude of Forced Oscillations in the Steady State ProblemsChapter Six Newton's Law of Gravitation Kepler's Laws of Planetary Motion Newton's Law of Universal Gravitation The Gravitational Force Between a Uniform Spherical Shell and a Particle The Gravitational Force between a Uniform Solid Sphere and a Particle The Gravitational Force on a Particle Which Is within a Uniform Spherical Shell Gauss' Law of Total Outward Normal Flux The Acceleration due to Gravity and the Mass of the Earth The Variation of the Acceleration of a Freely Falling Body with Its Distance from the Earth The Time to Fall from a Great Height to the Surface of the Earth The Gravitational Potential Due to the Earth Kepler's Law of Areal Velocity The Equation of the Path of a Particle under an Inverse Square Law of Force Kepler's Harmonic Law The Total Energy of a Planet Which is Moving in an Orbit ProblemsAnswersSubject Index