## Elements of Natural Philosophy, Volume 1 |

### From inside the book

Results 1-5 of 66

Page 7

... since , in the latter case , the direction of motion continually changes , the mere

must have in every such case additional data to thoroughly specify the motion .

... since , in the latter case , the direction of motion continually changes , the mere

**amount**of the velocity is not sufficient completely to describe the motion , and wemust have in every such case additional data to thoroughly specify the motion .

Page 9

... becomes the tangent at P. Hence the direction of acceleration is that of the

tangent to the curve thus described . The

change of velocity , and is therefore measured by the velocity of P in the curve PQ

. 36.

... becomes the tangent at P. Hence the direction of acceleration is that of the

tangent to the curve thus described . The

**amount**of acceleration is the rate ofchange of velocity , and is therefore measured by the velocity of P in the curve PQ

. 36.

Page 10

Hence the velocity of P is to that of A as OP to CA , i.e. as V to R ; and is therefore

equal to V 12 R R ' and this ( $ 35 ) is the

circular path ABD . 37. The whole acceleration in any direction is the sum of the ...

Hence the velocity of P is to that of A as OP to CA , i.e. as V to R ; and is therefore

equal to V 12 R R ' and this ( $ 35 ) is the

**amount**of the acceleration in thecircular path ABD . 37. The whole acceleration in any direction is the sum of the ...

Page 14

... arc of the hodograph represents the change of velocity of the moving point

during the corresponding time ; and also that the tangent to the hodograph is

parallel to the direction , and the velocity in the hodograph is equal to the

of the ...

... arc of the hodograph represents the change of velocity of the moving point

during the corresponding time ; and also that the tangent to the hodograph is

parallel to the direction , and the velocity in the hodograph is equal to the

**amount**of the ...

Page 22

To find the time and the

phase , let CA be equal to the greater half - amplitude . From A as centre , with AB

the less halfamplitude as radius , describe a circle . CB touching this circle ...

To find the time and the

**amount**of the maximum acceleration or retardation ofphase , let CA be equal to the greater half - amplitude . From A as centre , with AB

the less halfamplitude as radius , describe a circle . CB touching this circle ...

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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 evidently 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 perpendicular plane portion position potential practical pressure principle problem produce projection proportional quantity radius reference relative remain remarkable respectively rest resultant right angles rigid rotation round sides simple solid space spherical square straight strain stress suppose surface theory turned uniform unit velocity weight whole wire