Further Mechanics
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Description
Contents
Reviews
Language
English
ISBN
9781382018142
Front Cover
Imprint
Contents
1 Vectors I
Specifying a vector
Properties of vectors
Describing space using vectors
2 Vectors II
Vector product
Scalar triple product
Other geometrical uses of the vector product and the scalar triple product
Vector equation of a curve
Moments
Equivalent force systems and equilibrium
3 Differential Equations
Definitions and classification
Forming differential equations
First-order differential equations
Separation of variables
Homogeneous equations
First-order linear equations
Linear equations with constant coefficients
The complementary function and the particular integral
Second-order linear equations with constant coefficients
Vector differential equations
Simultaneous linear differential equations
Numerical methods
4 General Motion in One Dimension
Motion with variable mass
Variable forces
Examination Questions: Chapters 1 to 4
5 Impulses and ImpulsiVe Tensions
Oblique impact
Impulsive tensions
6 Oscillating Systems
Damped oscillations
Forced oscillations
Investigation
Resonance
7 Projectiles
Projectiles on an inclined plane
Air resistance
8 Motion of a Particle in a Plane
Cartesian coordinates
Polar resolutes of acceleration
Motion under a central force
Intrinsic coordinates
Examination Questions: Chapters 5 to 8
9 Stability of Equilibrium
Centre of mass
Stability of equilibrium
10 Moment of Inertia
Kinetic energy of rotation
Moment of inertia
Equation of rotational motion
Angular momentum
Uniform angular acceleration
Calculating the moment of inertia
Parallel and perpendicular axes theorems
Radius of gyration
Summary of standard results
11 Rotation about a Fixed Axis
Total energy of a rotating body
Work done by a couple
Relationship between work and energy
Compound pendulum
Reaction at the axis
Impulse and momentum
Conservation of angular momentum
12 General Motion of a Rigid Body in Two Dimensions
Particle model
Translational and rotational motion of the lamina
Angular momentum about a fixed point
Kinetic energy
Small oscillations of a system
Examination Questions: Chapters 9 to 12
Answers
Index
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