A Treatise on DynamicsMacmillan and Company, 1850 - 176 páginas |
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Términos y frases comunes
accelerating-force action angle angular velocity apply apse attraction axis body moving C₁ called center of gravity co-ordinates considered cos² curve D'Alembert's principle d2 x dt2 d²x definite integral described determine the motion direction distance dt dt dt dt dx dt dy dt² dv dt dx dt dx dx dx dy dy dt effective force ellipse equal equations of motion equilibrium expression fixed point force acting forces which act function geometrical given Hence impressed forces impulse increase instant integration internal forces interval magnitude mass method Mk² negative obtained orbit origin osculating plane particle perfect differential plane position principle problem quantities rest rigid body shews sin² space suppose t₁ takes place v₁ vis viva viva x₁ y₁ zero δι Ση
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Página 26 - NEWTON was able to formulate his great law of universal gravitation in these comprehensive words: "Every particle of matter in the universe attracts every other particle with a force directly as the masses of the two particles, and, inversely as the square of the distance which separates them." To show the nature of the attractive forces among these various particles, let us represent by m and m' the masses of two attracting bodies. We may conceive the body m to be composed of m particles, and the...
Página 46 - A body is projected with a velocity v in a direction making an angle a with the horizon...
Página 15 - MASS AND WEIGHT.— The mass of a body is the quantity of matter in it ; the weight of a body is due to the force of gravity acting upon this matter.
Página 146 - The moment of inertia about any axis is the sum of the products of the mass of each particle of the body into the square of its least distance from the axis.
Página 26 - GRAVITATION.* — Every particle of matter in the universe attracts every other particle of matter with a force directly proportional to its mass, and decreasing as the square of the distance Fig.
Página 9 - If two forces acting at a point be represented in magnitude and direction by the sides of a parallelogram, the resultant of these two forces will be represented in magnitude and direction by the diagonal of the parallelogram passing through this point.
Página 85 - Remembering that the resistance of the air varies as the square of the velocity, it might easily be shown that the strength should be at least eight times, instead of twice, as great. Passing to the question of power. The soaring of birds is a most important fact, of which no one who has taken the trouble to make observations has any doubt. Though it was lately the subject of a...
Página 144 - That is, if the resultant of all the external forces applied to a body is zero, the center of gravity will move in a straight line with uniform velocity. This is a generalization of Newton's First Law of Motion. REMARK. — It will be noticed that the above reasoning applies also to a non-rigid system of particles if the internal forces are in equilibrium among themselves. For example, so far as...
Página 166 - OA of the smaller circle to represent the direction of the incident ray, and let NAB be the direction of the normal to the surface at the point of incidence, so that 0 AN is the angle of incidence.