An Elementary Treatise on Mechanics

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G.Y. Van Debogert, 1854 - Mechanics - 197 pages

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Page 48 - Moment of a Force. — The moment of a force with respect to a point is the product of the force multiplied by the perpendicular distance from the given point to the direction of the force.
Page 50 - ... the sum of the moments of the forces which tend to turn the body in one direction must be equal to the sum of the moments of those which tend to turn it in the opposite direction about the same axis.
Page 127 - For, by the first of Kepler's laws, the areas described by the radius vector are proportional to the times, and when this is the case, by Art.
Page 48 - ... directions of the forces sensibly parallel : whence we must conclude, that the line of direction of the resultant of two parallel forces is in the plane of the forces, is parallel to the direction of the forces, and that the moment of the resultant, taken in reference to any point in the plane of the forces, is equal to the sum or difference of the moments of the components, according as they tend to turn the system in the same or opposite directions about the centre of moments.
Page 175 - ... two planets are to each other as the cubes of their mean distances from the sun.
Page 175 - Application of the preceding formulae to the motions of the planets. 368. Observation has established three facts respecting the motions of the planets, which, from their discoverer, are called Kepler's Laws. 1. The areas described by the radius vector of a planet are proportional to the times. 2. The orbit of a planet is an ellipse of which the center of the sun is one of the foci, 3. The squares of the times of revolution of the different planets are proportional to the cubes of their mean...
Page 37 - The point of application of the resultant of a system of parallel forces is called the centroid or center of the system of forces.
Page 16 - If a moving point possess simultaneously velocities which are represented in magnitude and direction by the two sides of a parallelogram drawn from a point, they are equivalent to a velocity which is represented in magnitude and direction by the diagonal of the parallelogram passing through the point.
Page 16 - To find the resultant of two parallel forces. The resultant is in the same plane with, and parallel to, the components. It is their sum or difference according as they act in the same or contrary directions; and in the latter case its direction is that of the greater component. To find its line of action by construction, proceed as follows : — Fig.
Page 133 - Comparing this value of c 2 r cos / with that of c, we have c' = c cos I. That is, the centrifugal force at any point on the earth's surface is equal to the centrifugal force at the equator, multiplied by the cosine of the latitude of the place.

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