the axis of rotation, and points out in the direction in which a right handed screw would advance, if the head of the screw is rotated with the body. (See Fig. .17a). The magnitude of this vector is dt referred as above.
Fig. . (a) If the head of a right handed screw rotates with the body, the screw advances in the direction of the angular velocity ωωωωω . If the sense (clockwise or anticlockwise) of rotation of the body changes, so does the direction of ωωωωω .
Fig. . (b) The angular velocity vector ωωωωω is directed along the fixed axis as shown. The linear velocity of the particle at P is v = ωωωωω × r .
It is perpendicular to both ω ω and r and is directed along the tangent to the circle described by the particle. We shall now look at what the vector product ωωωωω × r corresponds to. Refer to Fig. .
(b) which is a part of Fig. . reproduced to show the path of the particle P. The figure shows the vector ωωωωω directed along the fixed ( z –) axis and also the position vector r = OP of the particle at P of the rigid body with respect to the origin O.
Note that the origin is chosen to be on the axis of rotation. Now ωωωωω × r = ωωωωω × OP = ωωωωω × (OC + CP) But ωωωωω × OC = as ω ω is along OC Hence ωωωωω × r = ωωωωω × CP The vector ωωωωω × CP is perpendicular to ωωωωω , i.e. to the z -axis and also to CP , the radius of the circle described by the particle at P. It is therefore, along the tangent to the circle at P.
Also, the magnitude of ωωωωω × CP is ω (CP) since ωωωωω and CP are perpendicular to each other. We shall denote CP by ⊥ r and not by r , as we did earlier. Thus, ωωωωω × r is a vector of magnitude