for a × b can be put in a determinant form which is easy to remember. Example . Find the scalar and vector products of two vectors. a = and b = Answer ( ) ( ) = − = − Note = − ⊳ .
ANGULAR VELOCITY AND ITS RELATION WITH LINEAR VELOCITY In this section we shall study what is angular velocity and its role in rotational motion. We have seen that every particle of a rotating body moves in a circle. The linear velocity of the particle is related to the angular velocity. The relation between these two quantities involves a vector product which we learnt about in the last section.
Let us go back to Fig. . . As said above, in rotational motion of a rigid body about a fixed axis, every particle of the body moves in a circle, Fig.
. Rotation about a fixed axis. (A particle ( P ) of the rigid body rotating about the fixed (z-) axis moves in a circle with centre (C) on the axis.) which lies in a plane perpendicular to the axis and has its centre on the axis. In Fig.
. we redraw Fig. . , showing a typical particle (at a point P) of the rigid body rotating about a fixed axis (taken as the z -axis).
The particle describes a circle with a centre C on the axis. The radius of the circle is r , the perpendicular distance of the point P from the axis. We also show the linear velocity vector v of the particle at P. It is along the tangent at P to the circle.
Let P ′ be the position of the particle after an interval of time ∆ t (Fig. . ). The angle PCP ′ describes the angular displacement ∆ θ of the particle in time ∆ t .
The average angular velocity of the particle over the interval ∆ t is ∆ θ / ∆ t. As ∆ t tends to zero (i.e.