## Elements of Natural Philosophy, Volume 1 |

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Page 36

Let S

the body from its first position , without rotation , in a direction perpendicular to S ,

till S comes into the plane of its a second position . Then to get the body into 36 ...

Let S

**denote**a plane of the body , the two positions of which are parallel . Movethe body from its first position , without rotation , in a direction perpendicular to S ,

till S comes into the plane of its a second position . Then to get the body into 36 ...

Page 38

What we have

sometimes called , the rate of precession . The angular motions W , 12 are to one

another inversely as the distances of a point in the axis of the rolling cone from ...

What we have

**denoted**by 1 is the angular velocity of the precession , or , as it issometimes called , the rate of precession . The angular motions W , 12 are to one

another inversely as the distances of a point in the axis of the rolling cone from ...

Page 82

Hence at the instant when their velocities are equalized they move as one mass

with a momentum equal to the sum of the momenta of the two before impact .

That is to say , if v

...

Hence at the instant when their velocities are equalized they move as one mass

with a momentum equal to the sum of the momenta of the two before impact .

That is to say , if v

**denote**the common velocity at this instant , we have or ( M + M...

Page 83

or ( M + M ' ) v = MV + M'V ' , MV + M'V ' MUM ' if M , M '

two bodies , and V , V ' their velocities before impact . During this first period of

the impact the bodies have been , on the whole , coming into closer contact with ...

or ( M + M ' ) v = MV + M'V ' , MV + M'V ' MUM ' if M , M '

**denote**the masses of thetwo bodies , and V , V ' their velocities before impact . During this first period of

the impact the bodies have been , on the whole , coming into closer contact with ...

Page 99

... each equal to a TV , where a

velocity in it , and b the radius of the circular cross section of the ring . This is

proved by remarking that an infinitely narrow band from the outermost part of the

ring ...

... each equal to a TV , where a

**denotes**the radius of that circle , w the angularvelocity in it , and b the radius of the circular cross section of the ring . This is

proved by remarking that an infinitely narrow band from the outermost part of the

ring ...

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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