Elements of Theoretical MechanicsMacmillan, 1904 - 494 páginas |
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Termos e frases comuns
A₁ acceleration angular momentum angular velocity axes C₁ called centroid circle co-ordinates components constant cord cose couple crank curve cylinder denote determine diameter direction displacement distance dt dt ellipse ellipsoid equal and opposite equations of motion expressed fixed axis fixed point force F forces acting friction ft./sec funicular geometrically given hence homogeneous horizontal hyperbola initial velocity integration intersection kinetic energy length linear m₁ magnitude moment of inertia moments momentum moving mv² orbit origin oscillations parabola parallel forces pendulum perpendicular piston plane polygon position pressure principal axes principle radius of inertia radius vector reaction regarded represents resultant right angles rigid body rotation Show simple harmonic motion sine sphere straight line surface t₁ tangent tension tion translation triangle vertex vertical W₁ weight zero
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Página 29 - 'arth's orbit has an inclination towards changes,' you say." " The changes in the seasons, sir, are owing to ' the inclination of the earth's axis to the plane of its orbit.
Página 189 - Prove that the algebraic sum of the moments of two concurrent forces about any point in their plane is equal to the moment of their resultant about the same point.
Página 32 - ... directly as the unit of length, and inversely as the unit of time — a property which is also characteristic of the unit of velocity.
Página 468 - The bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides.
Página 211 - ... rupture, that the deflection of the solid is inconsiderable, and that the force W which causes it is perpendicular to the direction of the fibres, it follows that the conditions of equilibrium require that the algebraic sum of the forces in the direction of the fibres shall be equal to zero, and that the sum of the moments of all the forces with respect to the neutral line across the section at OP shall also be equal to zero.
Página 244 - ... that any system of forces acting on a rigid body can be reduced to a single force and a couple whose plane is at right angles to the direction of the force.
Página 174 - If two forces acting on a point are represented in magnitude and direction by two sides of a triangle, under what circumstances will the third side correctly represent their resultant? Forces of 20 and 10 act along the sides AB and BC respectively of an equilateral triangle ; find the magnitude of their resultant.
Página 359 - The Problem of Two Bodies. In the preceding discussion of the motion of a particle under the action of a central force, it has been assumed that the center of force is fixed. In the applications of the theory of central forces this assumption is in general not satisfied. Thus, in considering the motion of a planet around the sun, the force of attraction is, according to Newton's law of universal gravitation (Art.
Página 330 - V0, (6') which expresses the principle of the conservation of energy for a particle : the total energy, ie the sum of the kinetic and potential energies, remains constant throughout the motion ij the forces are conservative.
Página 29 - Time as measured by the apparent motion of the Vernal Equinox is called sidereal time. The sidereal day is the interval between two successive upper transits of the Vernal Equinox. The...