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Chapter
Centres of mass
Previously we have considered only the motion of particles, which are defined to be bodies whose size does not influence their motion. In the remaining chapters we shall be concerned with bodies whose size has...
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Chapter
Coplanar forces acting on a rigid body
In Chapter 4 we discussed the conditions which ensure that a rigid body is in equilibrium under a set of coplanar forces. In the present chapter we consider sets of coplanar forces acting on a rigid body which...
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Chapter
Momentum, impact and impulse
The work in this chapter is again based on Newton’s laws, which are first used to establish the principle of conservation of momentum for systems of particles. We also study how to predict the consequences of ...
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Chapter
Statics
The purpose of this chapter is to study the conditions under which particles and rigid bodies can rest in equilibrium, that is without moving. This branch of mechanics is called statics.
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Chapter
The motion of a rigid body about a fixed axis
The purpose of this final chapter is to investigate the motion of a rigid body turning about a fixed axis. We shall suppose that the axis is smooth, so that its bearings do not exert any frictional couple and ...
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Chapter
Energy, work and power
In order to use mathematics efficiently to deal with the mechanics of groups of particles, including rigid bodies, it is helpful first to use Newton’s laws to derive other principles. In this chapter, Newton’s...
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Book
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Chapter
Dimensions and bases
Again we consider displacements as a particular example of vectors and, in the first instance, restrict ourselves to displacements in a fixed plane.
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Chapter
Applications of vectors
The results of the preceding chapters are now used in three different circumstances. The principal application to be discussed in this book is the geometry of real space but some elementary kinematical and phy...
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Chapter
The vector product
The vector product (often called the cross product) of two vectors a and b, denoted by a × b, or sometimes a ∧ b, is defined to be a vector of magnitude |a| |b| sin θ, where θ is the angle contained between a and...
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Chapter
An introduction to vectors
In applying mathematics, particularly in the fields of physics and engineering, we need to be able to associate numbers with quantities that are important.
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Chapter
The scalar product
In any triangle ABC, the cosine rule states that
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Chapter
Differentiation and integration of vectors
We have already met vectors which depend on the value of a scalar variable; for example, if r is the position vector of a point on a straight line ...
