Principles Of MechanicsIn a sense this is a book for the beginner in mechanics, but in another sense it is not. From the time we make our first movements, crude ideas on force, mass, and motion take shape in our minds. This body of ideas might be reduced to some order at high school as crude ideas of geometry are reduced to order, but that is not the educational practice in North America. There is rather an accumulation of miscellaneous facts bearing on mechanics, some mathematical and some experimental, until a state is reached where the student is in danger of being repelled by the subject, as a chaotic jumble which is neither mathematics nor physics. This book is intended primarily for students at this stage. The authors ambition is to reveal mechanics as an orderly self-contained subject. It may not be quite so logically clear as pure mathematics, but it stands out as a model of clarity among all the theories of deductive science. The art of teaching consists largely in isolating difficulties and overcoming them one by one, without losing sight of the main problem while attending to the details. In mechanics, the main problem is the problem of equilibrium or motion under given forces the details are such things as the vector notation, the kinematics of a rigid body, or the theory of moments of inertia. If we rush straight at the main problem, we become entangled in the details and must retrace our steps in order to deal with them. If, on the other hand, we decide to settle all details first, we are apt to find them uninteresting because we do not see their connection with the main problem. A compromise is necessary, and in this book the compromise consists of the division into Plane Mechanics Part I and Mechanics in Space Part II. |
Contents
Section 23 | |
Section 24 | |
Section 25 | |
Section 26 | |
Section 27 | |
Section 28 | |
Section 29 | |
Section 30 | |
Section 9 | |
Section 10 | |
Section 11 | |
Section 12 | |
Section 13 | |
Section 14 | |
Section 15 | |
Section 16 | |
Section 17 | |
Section 18 | |
Section 19 | |
Section 20 | |
Section 21 | |
Section 22 | |
Section 31 | |
Section 32 | |
Section 33 | |
Section 34 | |
Section 35 | |
Section 36 | |
Section 37 | |
Section 38 | |
Section 39 | |
Section 40 | |
Section 41 | |
Section 42 | |
Section 43 | |
Section 44 | |
Other editions - View all
Common terms and phrases
acceleration angle angular momentum angular velocity axis of symmetry base point cable circular components cone consider constant angular velocity coordinates couple curve denote differential equation direction disk distance dynamical earth ellipsoid elliptic equal equations of motion equipollent external forces fixed point force system forces acting frame of reference friction function fundamental plane Galilean frame given gives gravity gyroscope Hence horizontal impulsive force integration kinetic energy length linear momentum Lorentz transformation magnitude mass center mathematical mechanics method moment of inertia moments of inertia Newtonian frame normal obtain orbit oscillations Oxyz parallel particle moving particle of mass perpendicular position of equilibrium position vector potential energy principal axes problem radius reaction relative result rigid body rotation scalar Show smooth solution spaceĀtime speed spherical pendulum statics trajectory triad unit vector vertical weight zero