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3. STATICS OF RIGID BODIES

In the preceding chapter it was assumed that each of the bodies considered could be treated as a single particie. Such a view, however, is not always possible, and a body, in generał, should be treated as a combination of a large number of particles. The size of the body will have to be taken into consideration, as well as the fact that forces will act on different particles and thus will have different points of application.

3.1 Moment of a force about a point and about an axis. Let us consider a force F acting on a rigid body (RB) (Fig.3.1). We shall define the moment of F about 0 as the vector product of r and F :

M₀ = r x F

(3.1)

According to the definition of the cross product (see eh. A.7) the moment M₀ must be perpendicular to the piane containing the point 0 and the force F, the sense of M₀ is furnished by the right-hand rule, and the magnitude of the moment M₀ is

M₍)= rFsinB = Fd

(3.2)

The magnitude of M₀ measures the tendency of the force F to make the RB rotate about a fixed axis directed along M₀.

Recalling (A.21), the cross-product (3.1) can be conveniently expressed by the following determinant

Thus, the rectangular components of M₀ are

M_x=yF_z-zF_y M_y = zF_x - xF_z M_z = xF_y - yF_x

StRB-1

(3.3)

(3.4)