Of Motion: An Elementary Treatise |
Other editions - View all
Common terms and phrases
accele acceleration produced angle apse axes axis called center of force CHAPTER circle co-ordinates complete oscillation conic section considered constant acceleration cos² curvature curve cycloid d2x dt2 described determine the motion Differential Calculus direction of motion distance ds dt dt dt dt² dx dy ellipse equal equation experiments fixed point focus force acting geometrical h²C h³u² horizontal hyperbola ideas impact impulse inclined plane initial direction initial position initial velocity initially at rest latus rectum Law of Motion mass material bodies matter and force measure moving point negative NEWTON obtained orbit origin parabola parallelogram parallelogram of forces particle path perpendicular point be moving quantity of matter radius vector semi-latus rectum shews sin² space passed Statics straight line string supposed tangent tion units of space v₁ velocity acquired vertex vis viva weight whence
Popular passages
Page viii - Chapter I. General principles of velocity and acceleration. Chapter II. Of the motion of a point in general Analytical expressions for velocities and accelerations in certain directions. Chapter III. Of the motion of a point affected by a constant acceleration, the direction of which is always the same. Chapter IV. Of the motion of a point affected by an acceleration, the direction of which always passes through a fixed point.
Page 11 - If two forces, acting at a point, be represented in magnitude and direction by the two sides of a parallelogram drawn from...
Page 104 - A person travelling eastward at the rate of 4 miles an hour, observes that the wind seems to blow directly from the north ; on doubling his speed the wind appears to come from the north-east ; determine the direction of the wind, and its velocity.
Page 2 - ... a string which passes over the highest horizontal line in the plane, and hangs vertically over it. Find the greatest and least weights which can be attached to the free end of the string consistently with equilibrium. 7. Define acceleration ; and assuming that the acceleration of gravity is 32 when a foot and a second are the units of space and time respectively, find its numerical value when a yard and a minute are taken as the units. 8. Explain the proposition of the parallelogram of velocities....
Page 120 - A pendulum is found to make 640 vibrations at the equator in the same time as...
Page 52 - Since it is an experimental fact that the point of application of a force may be transferred to any point of...
Page 68 - Gravitation is, that every particle of matter attracts every other particle with a force which varies directly as the mass of the attracting particle, and inversely as the square of the distance.
Page 101 - The measures of an acceleration and a velocity when referred to (a + b) ft., (m + ri)" and (a — b) ft, (m — n)" respectively, are in the inverse ratio of their measures when referred to (a — b} ft., (m — n...
Page 3 - ... the resultant velocity will be represented in magnitude and direction by the diagonal, drawn from that point, of the parallelogram constructed on the two straight lines as adjacent sides. This principle gives rise to applications similar to that deduced from the Parallelogram of Forces in Statics.
Page 125 - A seconds pendulum was too long on a given day by a quantity a ; it was then over-corrected so as to be too short by a during the next day...