Vectors and Rotors: With Applications

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Contents

a+BaB
105
Orthocentre of Triangle
106
The straight line equation
107
Mechanisms for drawing a straight line
108
The Hart Contraparallelogram
110
The Circle equation
111
Area of a triangle in coordinates
113
Angle between two straight lines
114
Coordinates of Masscentre from scalar product
115
Application to work done
116
The Peaucellier Cell
118
CHAPTER IV
119
Equality of two Rotors
120
Momental Areas
121
If the momental area of a Rotor is zero for three non collinear points the rotor itself vanishes
122
If two rotors have equal momental areas for all poles the rotors are equal If a system of Rotors has a resultant there is only one
123
Resultant of two intersecting Rotors Resultant of any concurrent system of Rotors
124
Coplanar Rotors first method of finding Resultant 125
125
EXERCISES IX
126
Couples definitions of a Couple and its Momental Area
127
EXERCISES X
134
Any system of rotors equivalent to a single rotor and
140
Rigid Bodies 187 Elastic Limit 188 Strain
155
Examples
173
Forces are Rotor Quantities
179
ExampleCrane
185
Stress
189
Measurement of Stress and Strain in rod under tension or compression
190
Hookes
191
Bodies supposed rigid
192
Weight of bars and friction neglected
193
that of line joining the centre points of pins
194
determination of Stresses
195
Stress diagram
196
Another Cantilever
197
Warren Girder
198
Web and Booms of Girder
199
Calculation of Stresses
200
Suspension Bridges
201
Funicular Polygon
202
Roofprincipal
203
Weight of bars
204
Wind pressure
205
Roof taking account of wind pressure EXERCISES XII
206
Theorem
207
Stress diagram by method of trial
208
Stress diagram by resolution of forces 210 Stress diagram by Moments 211 Rigid nonrigid and overrigid frames 212 Simple examples of overrigid fr...
209

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Page 21 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 29 - If the exterior angle of a triangle be bisected by a straight line which also cuts the base produced, the segments between the bisecting line and the extremities of the base have the same ratio which the other sides of the triangle have to one another...
Page 8 - If a straight line be divided into any two parts, the square on the whole line is equal to the squares on the two parts, together with twice the rectangle contained by the two parts.
Page 112 - ... is equal to the rectangle contained by the segments of the other.
Page 56 - ... are 8 in. Find the surface and volume of the greatest possible cylinder, of the same axis, that can be cut from the prism. Ex. 1634. The base of a right pyramid is a regular hexagon whose sides are 20 in., and the lateral faces are inclined to the base at an angle of 60. Find the volume. Ex. 1635. Lines joining the mid.points of opposite edges of a tetrahedron meet in a point and bisect each other. Ex. 1636. The altitude of a cone of revolution is 27 in., and its curved surface is 7 times the...
Page 29 - The parallelograms about the diameter of any parallelogram are similar to the whole, and to one another. Let...
Page 116 - Show that the work done by a force in producing a given displacement may be measured (1) by the product of the displacement and the component of the force in the direction of the displacement...
Page 181 - A, the algebraic sum of the moments of all the forces to the left of the section is zero, since there are no forces to the left.
Page 3 - In vector geometry, a vector quantity is represented diagrammatically by a line called a vector. The length of the line represents, to scale, the magnitude of the quantity, and its direction represents the direction in which the quantity acts.
Page 29 - L' and L" cut at right angles. (8) Prove that the three bisectors of the angles of a triangle meet in a point. (9) Show that the equation of a straight line in polar co-ordinates is of the form r = p cosec (в — ф). What is the meaning of "p...

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