A Treatise on DynamicsG. Bell, 1914 - 443 páginas |
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Términos y frases comunes
acceleration acting forces action angular momentum apse apse line axes axis bead body brachistochrone central orbit centre of force centre of gravity chain circle Coll component constant cos² curve cycloid diameter direction of motion distance elastic string ellipse equal equations of motion equiangular spiral equilibrium Exam fixed point focus given heavy particle Hence hodograph hyperbola impulse inclination kinetic energy latus rectum middle point moment of inertia momenta natural length normal obtain orbit parabola parallel particle is projected particle moves particle of mass path perpendicular position pressure prove radius of curvature radius vector relative rest revolving right angles ring rotation shew sin² slide small oscillation smooth horizontal plane sphere straight line surface Taking tangent tension time-flux tube uniform angular velocity uniformly varying inversely vertex vertical plane
Pasajes populares
Página 42 - Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it may be compelled by impressed forces to change that state.
Página 269 - Show that the moment of inertia of a body about any axis is equal to the moment of inertia about a parallel axis through the center of mass plus the product of the mass of the body and the square of the distance between the axes.
Página 92 - Shew that, according as the chain does or does not completely leave the floor, the velocity of the mass on finally reaching the floor again is the velocity due to a fall through a height where at = c2 (c + 3A).
Página 87 - Prove that in order to produce the greatest possible deviation in the direction of motion of a smooth billiard ball of diameter a by impact on another equal ball at rest, the former must be projected in a direction making an angle with the line, of length c, joining the two centers.
Página 244 - A particle is projected from a given point with a given velocity and is acted on by a given force to a fixed point.
Página 244 - Two particles of masses m and m' are connected by a string passing through a small hole at the vertex of a cone having its axis vertical and vertex uppermost. If m' hangs vertically, find the condition that m may describe a circle of radius c on the cone, and shew that if the particle be slightly disturbed it will oscillate about the circular path in the time ,, c(m + m') ) 71 '\ \3g(m' — mcosa)sinof
Página 322 - Discuss the motion that will ensue if at the moment slipping ceases the fixed ring be released and left free to move, and prove that during the time that the inner ring rolls half round the outer one the centre of the latter will be displaced a distance...
Página 308 - ... is the height of the door and a is the distance of either hinge from the nearest horizontal edge. 4. A wheel, 30 inches in diameter, which can rotate in a vertical plane about a horizontal axis through its centre O, carries a mass of J Ib. concentrated at a point P on its rim. The wheel is held with OP inclined at 30° above the horizontal and then released. Owing to a friction couple of constant magnitude L at the bearing, the first swing carries OP to a position 45° beyond the vertical.
Página 89 - Q, whose masses are m and m' respectively, are connected by an inextensible string which passes over a smooth fixed pulley. The heavier body P is perfectly elastic, and Q is inelastic ; they start from rest at the same distance a above a fixed horizontal plane, and when P impinges on the plane and rebounds with unchanged velocity, Q strikes against a fixed obstacle and is reduced to instantaneous rest. Determine the subsequent motion, and...
Página 246 - AB at right angles, and the intensity of which is inversely proportional to the cube of the distance of the particle from the line. The particle is projected with the velocity from infinity from a point P at a distance a from the nearest point O of the line in a direction perpendicular to OP, and inclined at the angle a to the plane AOP.