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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