of a top or a pedestal fan, one point and not one line, of the rigid body is fixed. In this case the axis is not fixed, though it always passes through the fixed point. In our study, however, we mostly deal with the simpler and special case of rotation in which one line (i.e. the axis) is fixed.
Thus, for us rotation will be about a fixed axis only unless stated otherwise. The rolling motion of a cylinder down an inclined plane is a combination of rotation about a fixed axis and translation. Thus, the ‘something else’ in the case of rolling motion which we referred to earlier is rotational motion. You will find Fig.
. (a) and (b) instructive from this point of view. Both these figures show motion of the same body along identical translational trajectory. In one case, Fig.
. (a), the motion is a pure translation; in the other case [Fig. . (b)] it is a combination of translation and rotation.
(You may try to reproduce the two types of motion shown, using a rigid object like a heavy book.) We now recapitulate the most important observations of the present section: The motion of a rigid body which is not pivoted or fixed in some way is either a pure translation or a combination of translation and rotation. The motion of a rigid body which is pivoted or fixed in some way is rotation. The rotation may be about an axis that is fixed (e.g. a ceiling fan) or moving (e.g.
an oscillating table fan [Fig. . (b)]). We shall, in the present chapter, consider rotational motion about a fixed axis only.
. CENTRE OF MASS We shall first see what the centre of mass of a system of particles is and then discuss its significance. For simplicity we shall start with a two particle system. We shall take the line joining the two particles to be the x - axis.
Fig. . Let the distances of the two particles be x and x respectively from some origin O. Let m and m be respectively the