## Elements of Natural Philosophy, Part 1 |

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Page 31

Th is , a body revolve in succession through equal angles , but in opposite

directions , about two A B parallel

translation in one plane can be compounded into an equal rotation about a

different

Th is , a body revolve in succession through equal angles , but in opposite

directions , about two A B parallel

**axes**, it finally ... so that a rotation and atranslation in one plane can be compounded into an equal rotation about a

different

**axis**. Page 32

From this it immediately follows , that any displacement of a rigid solid , which is

in directions wholly perpendicular to a fixed line , may be produced by the rolling

of a cylinder fixed in the solid on another cylinder fixed in space , the

From this it immediately follows , that any displacement of a rigid solid , which is

in directions wholly perpendicular to a fixed line , may be produced by the rolling

of a cylinder fixed in the solid on another cylinder fixed in space , the

**axes**of the ... Page 34

Hence the body may pass from any one position to any other by a definite

amount of rotation about a definite

simultaneous rotations about any number of

compounded ...

Hence the body may pass from any one position to any other by a definite

amount of rotation about a definite

**axis**. And hence , also , successive orsimultaneous rotations about any number of

**axes**through the fixed point may becompounded ...

Page 35

Let OA , OB be two

w , respectively . ... to the angular velocities about these

the parallelogram of which these are contiguous sides is the resultant

Let OA , OB be two

**axes**about which a body revolves with angular velocities w ,w , respectively . ... to the angular velocities about these

**axes**— the diagonal ofthe parallelogram of which these are contiguous sides is the resultant

**axis**. Page 36

tending to produce rotation about a perpendicular

change of direction of the

the angular velocity . 109. If a pyramid or cone of any form roll on a similar

pyramid ...

tending to produce rotation about a perpendicular

**axis**, the result will be achange of direction of the

**axis**about which the body revolves , but no change inthe angular velocity . 109. If a pyramid or cone of any form roll on a similar

pyramid ...

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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