First Lessons in Theoretical Mechanics |
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... circle , and a few articles and examples , occurring , for the most part , towards the end of the book . It will be proper to observe here that a good deal of choice has been exercised both as to the contents of the book , and as to the ...
... circle , and a few articles and examples , occurring , for the most part , towards the end of the book . It will be proper to observe here that a good deal of choice has been exercised both as to the contents of the book , and as to the ...
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... circle , something more is given than the motion of a point ; the treatment is necessarily imperfect , but I hope enough is done to throw some light on the motion round a fixed axis of a body symmetrical to a plane at right angles to ...
... circle , something more is given than the motion of a point ; the treatment is necessarily imperfect , but I hope enough is done to throw some light on the motion round a fixed axis of a body symmetrical to a plane at right angles to ...
Page 19
... circle . ( c ) By similar reasoning it may be shown that the centre of gravity of any parallelogram is at the point of intersection of the diagonals . ( d ) It can be shown in like manner that the centre of gravity of a triangle can be ...
... circle . ( c ) By similar reasoning it may be shown that the centre of gravity of any parallelogram is at the point of intersection of the diagonals . ( d ) It can be shown in like manner that the centre of gravity of a triangle can be ...
Page 36
... circle , a parallelogram , a triangle , a prism , a cylinder , a pyramid , a cone , a sphere , all the bodies being of uniform density . 10. In Ex . 8 ( p . 20 ) show that the result may be obtained by treating the body as if made up of ...
... circle , a parallelogram , a triangle , a prism , a cylinder , a pyramid , a cone , a sphere , all the bodies being of uniform density . 10. In Ex . 8 ( p . 20 ) show that the result may be obtained by treating the body as if made up of ...
Page 65
... circle cutting B C in c ; make the angle CBD equal to ACB ; then DB will equal D C ( Eucl . i . 6 ) , and ADB is the position of the thread . For if a vertical line N D W be drawn through D , it is plain that the angles ADN and BD N are ...
... circle cutting B C in c ; make the angle CBD equal to ACB ; then DB will equal D C ( Eucl . i . 6 ) , and ADB is the position of the thread . For if a vertical line N D W be drawn through D , it is plain that the angles ADN and BD N are ...
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Common terms and phrases
absolute units accelerative effect angle of friction angular velocity axis axle body moves centre of gravity centrifugal force coefficient of friction compression consequently couple cubic cylinder denote density described determined distance draw effect of gravity elastic energy equation equilibrium exerted expended fall feet and seconds foot-pounds force of gravity forces acting given gravitation units Hence horizontal inclined plane inertia instant last article last question length machine mass mercury modulus moment of inertia momentum motion mutual action opposite directions oscillation parallel forces parallelogram pendulum piston position pound principle of moments radius radius of gyration reaction resistance respectively rest resultant right angles rotation round screw specific gravity square inch student suppose surface thread three forces triangle turn uniform acceleration units act vertical line vessel weight
Popular passages
Page 187 - Whatever draws or presses another is as much drawn or pressed by that other. If you press a stone with your finger, the finger is also pressed by the stone. If a horse draws a stone tied to a rope, the horse (if I may so say) will be equally drawn back towards the stone...
Page 186 - 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.
Page 187 - Change of momentum is proportional to the impressed moving force, and takes place along the straight line in which that force is impressed.
Page 110 - Each wagon contains two and a quarter cubic yards. The result is, that each man has to lift nearly twenty tons weight of earth on a shovel over his head into a wagon. The height of the lifting is about six feet. This is taking it at fourteen sets a day ; but the navvies sometimes contrive to get through sixteen sets, and there are some men who will accomplish that astonishing quantity of work by three or four o'clock in the afternoon — a result, I believe, which is not nearly equalled by the workmen...
Page 160 - ... the resultant velocity will be represented in magnitude and direction by the diagonal, drawn from that point, of the parallelogram constructed on the two straight lines as adjacent sides.
Page 50 - ... the sum of the moments of the forces which tend to turn the body in one direction must be equal to the sum of the moments of those which tend to turn it in the opposite direction about the same axis.
Page 187 - To every action there is always opposed an equal reaction; or, the mutual actions of two bodies on each other are always equal and directed to contrary parts.
Page 92 - Every engineer knows that the work done by a force has to be measured by multiplying together the force and the distance through which its point of application moves forward.
Page 3 - The ratio of the mass of any quantity of a substance to the mass of an equal volume of some standard substance. In the case of solids and liquids the latter is chosen as water at 4° C.
Page 110 - set is a number of wagons — in fact, a train. There are two men to a wagon. If the wagon goes out fourteen times, each man has to fill seven wagons in the course of the day. Each wagon contains two and a quarter cubic yards. The result is, that each man has to lift nearly twenty tons weight of earth on a CHAP, shovel over his head into a wagon.