# Elementary Plane Rigid Dynamics

## 1st Edition

**Author:**H. W. Harkness

**eBook ISBN:**9781483274300

**Imprint:**Academic Press

**Published Date:**1st January 1964

**Page Count:**204

## Description

Elementary Plane Rigid Dynamics focuses on the basic ideas of particle dynamics, including center of gravity, inertia, friction, and oscillations.

The publication first offers information on the motion of a rigid body around a fixed axis. Discussions focus on moment of inertia for a sphere for an axis through its center of gravity; moment of inertia of a cylinder for an axis through its center of gravity and normal to its axis of figure; and moment of inertia of a rectangular parallelepiped for an axis normal to one of its faces and through its center of gravity.

The text then elaborates on the general plane motion of a rigid body and some special problems involving friction. Topics include belt and rope friction, power transmitted by a flat disk coupling, friction in a flat step bearing, meaning of the general torque equation for plane motion, superelevation of the outer rail on a railway curve, kinetic energy, and equilibrium. The book takes a look at undamped simple harmonic motion and damped and forced oscillations, including vibrations with damping, compound pendulum, and amplitude of forced oscillations in the steady state.

The publication is a valuable source of data for students interested in plane rigid dynamics.

## Table of Contents

Preface

Chapter 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

Problems

Chapter 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

Problems

Chapter 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

Problems

Chapter 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

Problems

Chapter 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

Problems

Chapter 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

Problems

Answers

Subject Index

## Details

- No. of pages:
- 204

- Language:
- English

- Copyright:
- © Academic Press 1964

- Published:
- 1st January 1964

- Imprint:
- Academic Press

- eBook ISBN:
- 9781483274300