An Elementary Treatise on Analytic Mechanics: With Numerous Examples |
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Common terms and phrases
acceleration angle angle of friction angular velocity applied axes axis axle beam centre of gravity circle co-ordinates coefficient of friction components concurring forces constant cord cos² couple curve d²x denote density diameter distance dx dy equal equation feet Find the centre forces acting friction fulcrum given Hence inclined plane inertia kinetic latus rectum length lever magnitude and direction mass mechanical advantage moment of inertia motion moving oscillation P₁ parabola parallel forces particle pendulum perpendicular point of application position of equilibrium pressure projection pulley radius vector resistance resolved respectively rest resultant rigid body rotation sin² smooth sphere Statics straight line string suppose surface tangent tension three forces tion triangle uniform vertex vertical virtual displacement virtual velocities vis viva weight wheel πα
Popular passages
Page 290 - Change of motion is proportional to the force applied and takes place in the direction of the straight line in which the force acts.
Page 485 - The attraction of a uniform spherical surface on an external point is the same as if the whole mass were collected at the centre.
Page 245 - Let P be the position of the particle at any time t, /the resultant acceleration acting always along OP, O being a fixed point in the line of motion.
Page 290 - To every action there is always an equal and contrary reaction ; or, the mutual actions of any two bodies are always equal and oppositely directed in the same straight line.
Page 24 - The Parallelogram of Forces. — If two forces acting at a point be represented in magnitude and direction by the adjacent sides of a parallelogram, the resultant...
Page 329 - A particle is projected from a given point in a given direction and with...
Page 292 - Since forces are measured by the changes of motion they produce, and their directions assigned by the directions in which these changes are produced ; and since the changes of motion of one and the same body are in the directions of, and proportional to, the changes of velocity — a single force, measured by the resultant change of velocity, and in its direction, will be the equivalent of any number of simultaneously acting forces.
Page 181 - The parts of the lever, into which the fulcrum divides it, are called the arms of the lever. When the arms are in the same straight line, it is called a straight lever, otherwise a bended, or more commonly, a bent lever.
Page 27 - If a number of forces acting at a point can be represented in magnitude and direction by the sides of a closed polygon taken...
Page 367 - A railway train is moving smoothly along a curve at the rate of 60 miles an hour, and in one of the carriages a pendulum, which would ordinarily oscillate seconds, is observed to oscillate 121 times in 2 min.