## Elements of Natural Philosophy |

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Page 13

The same is true of moments of forces and of moments of momentum , as defined

in Chapter II . First , consider two component motions , AB and AC , and let AD be

their resultant ( 8 31 ) . Their half - moments round the point o are

The same is true of moments of forces and of moments of momentum , as defined

in Chapter II . First , consider two component motions , AB and AC , and let AD be

their resultant ( 8 31 ) . Their half - moments round the point o are

**respectively**... Page 23

... by the angles QCS and SCQ

been usefully applied by the tidal committee of the British Association for a

mechanical tideindicator ( compare § 77 below ) . An arm CQ turning round C

carries an ...

... by the angles QCS and SCQ

**respectively**. This geometrical construction hasbeen usefully applied by the tidal committee of the British Association for a

mechanical tideindicator ( compare § 77 below ) . An arm CQ turning round C

carries an ...

Page 36

Let OA , OB be two axes about which a body revolves with angular velocities w ,

w ,

Draw la , IB perpendicular to OA , OB

Let OA , OB be two axes about which a body revolves with angular velocities w ,

w ,

**respectively**. With radius unity describe the arc AB , and in it take any point I .Draw la , IB perpendicular to OA , OB

**respectively**. Let the rotations about the ... Page 37

IP , Ig , parallel to OB , OA

the parallelogram Ipog , we have Og . Iß = Op . La . Hence Og : Op : : W , : W In

words , if on the axes OA , OB , we measure off from " , lines Op , Oq , proportional

...

IP , Ig , parallel to OB , OA

**respectively**. Then , expressing in two ways the area ofthe parallelogram Ipog , we have Og . Iß = Op . La . Hence Og : Op : : W , : W In

words , if on the axes OA , OB , we measure off from " , lines Op , Oq , proportional

...

Page 47

Let OX and OZ be the directions of maximum elongation and maximum

contraction

and A , the same point of the altered body , so that 0A , = a . OA . Now , if we take

OC = 0A ...

Let OX and OZ be the directions of maximum elongation and maximum

contraction

**respectively**. Let A be any point of the body in its primitive condition ,and A , the same point of the altered body , so that 0A , = a . OA . Now , if we take

OC = 0A ...

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acceleration according acting action amount angle angular applied attraction axes axis body called centre centre of inertia circle component condition consider constant corresponding couple course curvature curve denote density described determined direction displacement distance divided effect elastic elements energy equal equations equilibrium expression figure fixed fluid force friction give given gravity harmonic Hence important increase infinitely small instant interval kinetic length less mass matter mean measured method motion moving natural normal observation opposite parallel particle passing path period perpendicular plane portion position potential practical pressure principle produce projection proportional quantity radius reference relative remain remarkable resistance respectively rest resultant right angles rigid rotation round sides simple solid space spherical square straight strain stress suppose surface theory turned uniform unit velocity vertical weight whole wire