## Elements of Natural Philosophy |

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Page 23

( since the

ece is constant ) , and revolves with the same

therefore the resultant motion is simple harmonic , of amplitude cs , and of epoch

...

( since the

**angular**velocities of CQ and CQ are equal , and therefore the angleece is constant ) , and revolves with the same

**angular**velocity as CQ or cQ ' ; andtherefore the resultant motion is simple harmonic , of amplitude cs , and of epoch

...

Page 27

Also we see generally that the composition of any number of simple harmonic

motions in any directions and of any periods , may be effected by adding their

components in each of any three rect .

motion is ...

Also we see generally that the composition of any number of simple harmonic

motions in any directions and of any periods , may be effected by adding their

components in each of any three rect .

**angular**directions . The final resultantmotion is ...

Page 32

4 B O mine the relation between the

position . Evidently the instantaneous direction of motion of B is transverse to AB ,

and of D transverse to CDhence if AB , CD produced meet in 0 , the motion of BD

is ...

4 B O mine the relation between the

**angular**velocities of AB and CD in anyposition . Evidently the instantaneous direction of motion of B is transverse to AB ,

and of D transverse to CDhence if AB , CD produced meet in 0 , the motion of BD

is ...

Page 36

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

w , respectively . With radius unity describe the arc AB , and in it take any point 1 .

Draw la , IB perpendicular to 0A , OB respectively . Let the rotaA tions about the ...

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 1 .

Draw la , IB perpendicular to 0A , OB respectively . Let the rotaA tions about the ...

Page 37

In words , if on the axes OA , OB , we measure off from " O lines Op , Og ,

proportional respectively to the

of the parallelogram of which these are contiguous sides is the resultant axis .

Again , if ...

In words , if on the axes OA , OB , we measure off from " O lines Op , Og ,

proportional respectively to the

**angular**velocities about these axes - the diagonalof the parallelogram of which these are contiguous sides is the resultant axis .

Again , if ...

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### Common terms and phrases

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 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