## Elements of Natural Philosophy |

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Page 67

A

. The Moment of a

in their plane , and is therefore equal to the product of either force into the ...

A

**Couple**is a pair of equal forces acting in dissimilar direc . tions in parallel lines. The Moment of a

**couple**is the sum of the moments of its forces about any pointin their plane , and is therefore equal to the product of either force into the ...

Page 68

The work done by a force , or by a

the product of the moment of either into the angle ( in circular measure ) through

which the body acted on turns , if the moment remains the same in all positions ...

The work done by a force , or by a

**couple**, upon a body turning about an axis , isthe product of the moment of either into the angle ( in circular measure ) through

which the body acted on turns , if the moment remains the same in all positions ...

Page 77

... is equal to the moment of the

gives uniform acceleration of angular velocity ; or w

that the corresponding by s Force formula for linear acceleration is š = 0 <M 237 .

... is equal to the moment of the

**couple**about that axis Hence a constant**couple**gives uniform acceleration of angular velocity ; or w

**Couple**Me By $ 178 we seethat the corresponding by s Force formula for linear acceleration is š = 0 <M 237 .

Page 134

Then if Q be the

' _ sin which gives the

fibres be taken into account , it will be sensibly equal to 0 ( since the greatest ...

Then if Q be the

**couple**tending to turn the bar , and Wits weight , we have O - Wa' _ sin which gives the

**couple**in terms of the deflection 0 . If the torsion of thefibres be taken into account , it will be sensibly equal to 0 ( since the greatest ...

Page 141

Let three forces act in consecutive directions round a triangle , DEF , and be

represented respectively by its sides : they are i not in equilibrium , but are

equivalent to a

EF , and ...

Let three forces act in consecutive directions round a triangle , DEF , and be

represented respectively by its sides : they are i not in equilibrium , but are

equivalent to a

**couple**. To prove this , through D draw DH , equal and parallel toEF , and ...

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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 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 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