vi MECHANICAL ENGINEERING PRINCIPLES8 Bending of beams 103
8.1 Introduction 1038.2 To prove thatσ
y=M
I=E
R1038.3 Worked problems on
the bending of beams 1059 Torque 109
9.1 Couple and torque 109
9.2 Work done and power
transmitted by a constant torque 110
9.3 Kinetic energy and
moment of inertia 112
9.4 Power transmis-
sion and efficiency 11610 Twisting of shafts 120
10.1 Introduction 120
10.2 To prove thatτ
r=T
J=Gθ
L120
10.3 Worked problems on
the twisting of shafts 122Assignment 3 126Part 2 Dynamics 127
11 Linear and angular motion 127
11.1 The radian 127
11.2 Linear and angular velocity 127
11.3 Linear and angular acceleration 129
11.4 Further equations of motion 130
11.5 Relative velocity 132
12 Linear momentum and impulse 136
12.1 Linear momentum 136
12.2 Impulse and impulsive forces 139
13 Force, mass and acceleration 144
13.1 Introduction 144
13.2 Newton’s laws of motion 144
13.3 Centripetal acceleration 147
13.4 Rotation of a rigid
body about a fixed axis 149
13.5 Moment of inertia (I) 149
14 Work, energy and power 153
14.1 Work 153
14.2 Energy 157
14.3 Power 159
14.4 Potential and kinetic energy 162
14.5 Kinetic energy of rotation 165
Assignment 4 16915 Friction 170
15.1 Introduction to friction 170
15.2 Coefficient of friction 170
15.3 Applications of friction 172
15.4 Friction on an inclined plane 173
15.5 Motion up a plane with
the pulling forceP
parallel to the plane 173
15.6 Motion down a plane
with the pulling force
P parallel to the plane 174
15.7 Motion up a plane due
to a horizontal forceP 175
15.8 The efficiency of a screw jack 17716 Motion in a circle 182
16.1 Introduction 182
16.2 Motion on a curved banked track 184
16.3 Conical pendulum 185
16.4 Motion in a vertical circle 187
16.5 Centrifugal clutch 18917 Simple harmonic motion 191
17.1 Introduction 191
17.2 Simple harmonic motion (SHM) 191
17.3 The spring-mass system 192
17.4 The simple pendulum 194
17.5 The compound pendulum 195
17.6 Torsional vibrations 19618 Simple machines 198
18.1 Machines 198
18.2 Force ratio, movement
ratio and efficiency 198
18.3 Pulleys 200
18.4 The screw-jack 202
18.5 Gear trains 203
18.6 Levers 205Assignment 5 209Part 3 Heat transfer and fluid mechanics 21119 Heat energy and transfer 211
19.1 Introduction 211
19.2 The measurement of temperature 212
19.3 Specific heat capacity 212
19.4 Change of state 214
19.5 Latent heats of fusion
and vaporisation 215
19.6 A simple refrigerator 217
19.7 Conduction, convec-
tion and radiation 217
19.8 Vacuum flask 218