Newtonian Dynamics

An Introduction

Richard Fitzpatrick

• Publisher: CRC Press
• Year: 2021
• Print ISBN: 9781032056661
• eBook ISBN: 9781000509571
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Astronomy & Astrophysics

This textbook provides a comprehensive review of Newtonian dynamics at a level suitable for undergraduate physics students. It demonstrates that Newton's three laws of motion, combined with a few simple force laws, not only can describe the motions of everyday objects observed on the surface of the Earth, but can also account for the motions of celestial objects seen in the sky. It helps bridge the problematic transition between elementary physics courses and upper-division physics courses. The book starts off at a level suitable for undergraduate (freshman) physics students and very gradually increases, until, toward the end, it approaches (but does not quite reach) a level characteristic of a graduate (senior) physics course.

Each chapter of the book ends with a large number of numerical and analytical exercises and, in all appropriate cases, the final answers to the exercises are specified. The large number of exercises will allow students to accurately test their understanding of the material presented in the book, ideal for students who are self-studying or are taking classes remotely.

Key Features:

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• Provides a brief and accessible introduction to a complex topic

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• Contains a more thorough treatment of the motions of heavenly bodies than conventional elementary mechanics texts

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• Provides a wealth of end-of-chapter exercises to test understanding

Richard Fitzpatrick is a Professor of physics at the University of Texas at Austin, USA, where he has been a faculty member since 1994. He is a member of the Royal Astronomical Society, a fellow of the American Physical Society, and the author of several textbooks.

CHAPTER 1 Measurement and Units

DOI: 10.1201/9781003198642-1

1.1 Mks Units

The first principle of any exact physical science is measurement. In Newtonian dynamics, there are three fundamental quantities that are subject to measurement:

1. Intervals in space; that is, length.
2. Quantities of inertia, or mass, possessed by various bodies.
3. Intervals in time.

Any other type of measurement in Newtonian dynamics can (effectively) be reduced to some combination of measurements of these three quantities.

Each of the three fundamental quantities—length, mass, and time—is measured with respect to some convenient standard. The system of units currently used by most scientists and engineers is called the mks system—after the first initials of the names of the units of length, mass, and time, respectively, in this system. That is, the meter, the kilogram, and the second.

The mks unit of length is the meter (symbol: m). The meter was formerly the distance between two scratches on a platinum-iridium alloy bar kept at the International Bureau of Weights and Measures in Sèvres, France, but is now defined as the distance travelled by light in vacuum in 1/299792458 seconds (Wikipedia contributors 2021).

The mks unit of mass is the kilogram (symbol: kg). The kilogram was formally defined as the mass of a platinum-iridium alloy cylinder kept at the International Bureau of Weights and Measures in Sèvres, France, but is now defined in such a manner as to make Planck’s constant take the value $6.62607015\times {10}^{-34}$ when expressed in mks units (Wikipedia contributors 2021).

The mks unit of time is the second (symbol: s). The second was formerly defined in terms of the Earth’s rotation, but is now defined as the time required for 9192631770 complete oscillations associated with the transition between the two hyp...

Table of contents

• Cover Page
• Half-Title Page
• Title Page
• Copyright Page
• Contents
• Preface
• Acknowledgements
• Chapter 1 ◾ Measurement and Units
• Chapter 2 ◾ Motion in One Dimension
• Chapter 3 ◾ Motion in Three Dimensions
• Chapter 4 ◾ Newton’s Laws of Motion
• Chapter 5 ◾ Conservation of Energy
• Chapter 6 ◾ Conservation of Momentum
• Chapter 7 ◾ Circular Motion
• Chapter 8 ◾ Rotational Motion
• Chapter 9 ◾ Angular Momentum
• Chapter 10 ◾ Statics
• Chapter 11 ◾ Oscillatory Motion
• Chapter 12 ◾ Rotating Reference Frames
• Chapter 13 ◾ Newtonian Gravity
• Chapter 14 ◾ Orbital Motion
• Chapter 15 ◾ Gravitational Potential Theory
• Appendix A  ◾ Useful Mathematics
• Bibliography
• Index