The Elements of Mechanics: Comprehending Statics and Dynamics. With a Copious Collection of Mechanical Problems. Intended for the Use of Mathematical Students in Schools and Universities ... |
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acceleration accelerative force angle angular velocity applied axle beam Calc called catenary centre of gravity centre of oscillation centrifugal force co-ordinates components concurring forces consequently consider cord curve cycloidal differential direction distance dt dt dx dy equa equal equation equilibrating equilibrium expression fixed axis fixed point forces acting funicular given hence horizontal line impulse inclined plane inertia integral intensity length lever mass moment of inertia opposite P₁ P₂ parallel forces parallelogram of forces particle pendulum perpendicular point of application polygon position pressure principal axes PROBLEM projection pulley quantities radius radius of gyration represent resistance respect resultant revolve rotation solid body space string substituting suppose surface suspended system of forces tangent tension theory tion triangle v₁ vertical W₁ weight wheel whole
Popular passages
Page 186 - a added to either of these expressions will give the distance of the centre of oscillation from the point of suspension. 5. To determine the centre of oscillation of a cone suspended at its vertex. Putting (as in ex. 3, page
Page 178 - To determine the moment of inertia of a solid of revolution, with respect to the fixed axis, it will be most convenient to view the solid as generated by the motion of a circle which continues always perpendicular to the fixed axis while the centre describes this axis, as explained at page
Page 157 - that this angular velocity varies inversely as the square of the distance of the body from the centre of force. If we substitute in (2) the value of
Page 85 - the Lever, the Wheel and axle, the Pulley, the Inclined Plane, the Screw, and the Wedge. The Lever
Page 161 - The squares of the times of revolution are as the cubes of the mean distances from the sun, or as the cubes of the major axes of the orbits.
Page 152 - is very remarkable, inasmuch as it proves that the time of descent to the lowest point is always the same from whatever point in the curve the body begins to descend. The oscillations in a cycloid are, therefore, always isochronal. The cycloidal pendulum must oscillate between the two equal cycloidal cheeks SB,
Page 56 - that the distance of the centre of gravity from the centre of the circle is a fourth, proportional to the arc, the radius, and the chord of the arc.
Page 154 - that the periodic time varies as the square root of the altitude of the conical surface described, whatever be the length of the pendulum, or the radius of the base of the cone. We have seen (prob. I.) that the time in which a pendulum of length
Page 34 - and from this we may get the value of cos. a, by means of the first of (13). It thus appears that when a flexible cord, or chain of given length, is suspended from two points, at a given distance from each other, in the same horizontal line,
Page 117 - (109.) When a body is placed on an inclined plane the force of gravity produces a certain pressure, represented by the weight of the body : if we resolve this vertical pressure P in two directions, the one along the plane , and the other perpendicular to it, the former component will be P sin.