An Elementary Treatise on Mechanics |
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Common terms and phrases
acceleration algebraic sum angle angular velocity assumed axes axis axle becomes body central force centre of gravity centre of moments centrifugal force chord circle circumference co-ordinates components conceive constant force cord curve denote diameter distance ellipse equal particles equal to zero equation equilibrium force F force of gravity forces applied formula friction generatrix given forces Hence hyperbola impart impressed force inclined plane indefinitely small inertia initial velocity length lever lines of direction M₁ moment of inertia motion move orbit P₁ parabola parallel forces Pcos perpendicular point of application power and weight power-arm proportional pulleys R₁ radius represent resistance respectively resultant revolution revolve rope rotation S₁ similar triangles simple pendulum space accomplished substitution supposed tangent tion unit V₁ velocity acquired vertical vibration virtual velocity W₁ whence ΣΡ
Popular passages
Page 226 - ... is equal to the square root of the quotient obtained by dividing the...
Page 100 - These simple machines are the lever, the wheel and axle, the pulley, the inclined plane, the wedge, and the screw.
Page 55 - Pz, are called the moments of R and P respectively referred to this plane. The result contained in this equation may then be thus enunciated : The moment of the resultant of a system of parallel forces , with respect to any plane whatever ', is equal to the sum of the moments of the forces with respect to the same plane. Since the forces are affected with the positive or negative sign, according to the sense in which they act, and the signs of the co-ordinates of the points of application are also...
Page 178 - The third, viz. that the squares of the periodic times are proportional to the cubes of the mean distances...
Page 214 - The moment of inertia of a body with respect to any axis is equal to its moment of inertia with respect to a parallel...
Page 179 - The third and last, that the squares of the periodic times of the planets are as the cubes of their mean distances from the sun.
Page 178 - ... that the squares of the periodic times are proportional to the cubes of the mean distances of the planets from the Sun.
Page 33 - When three forces acting at a point are in equilibrium, each force is proportional to the sine of the angle between the other two.
Page 61 - Art. 16, the moment of the resultant with respect to any axis perpendicular to the plane of the forces is equal to the algebraic sum of the moments of the component forces, with respect to the same axis.
Page 199 - That is, that component of the centrifugal force at any point, which opposes the force of gravity, is equal to the centrifugal force at the equator, multiplied by the square of the cosine of the latitude of the place.