## Elements of Natural Philosophy, Part 1 |

### From inside the book

Results 6-10 of 86

Page 10

... point we have

components of the velocity in three rectangular directions , at any time , or , as is

most commonly the case , for any position ; the determination of IO

PRELIMINARY .

... point we have

**given**the whole velocity and its direction , or simply thecomponents of the velocity in three rectangular directions , at any time , or , as is

most commonly the case , for any position ; the determination of IO

PRELIMINARY .

Page 11

This is true also if the total acceleration and its direction at every instant , or

simply its rectangular components , be

direction , as well as the position of the point , at any one instant be

these are in ...

This is true also if the total acceleration and its direction at every instant , or

simply its rectangular components , be

**given**, provided the velocity and itsdirection , as well as the position of the point , at any one instant be

**given**. Butthese are in ...

Page 13

It follows also , that if velocities , in different directions all in one plane , be

successively

resultant , the moment of its velocity at any time is the sum of the moments of all

the velocities ...

It follows also , that if velocities , in different directions all in one plane , be

successively

**given**to a moving point , so that at any time its velocity is theirresultant , the moment of its velocity at any time is the sum of the moments of all

the velocities ...

Page 14

The proof will be

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 ...

The proof will be

**given**immediately . It was shown ( $ 35 ) that an arc of thehodograph 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 ...

Page 16

A further instance of this use of the idea of angular velocity may now be

solve the problem of finding the hodograph ( § 35 ) for any case of motion in

which the acceleration is directed to a fixed point , and varies inversely as the ...

A further instance of this use of the idea of angular velocity may now be

**given**, tosolve the problem of finding the hodograph ( § 35 ) for any case of motion in

which the acceleration is directed to a fixed point , and varies inversely as the ...

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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 evidently experience 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 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