masses of the two Fig. . (a) Motion of a rigid body which is pure translation. Fig.
. (b) Motion of a rigid body which is a combination of translation and rotation. Fig . (a) and .
(b) illustrate different motions of the same body. Note P is an arbitrary point of the body; O is the centre of mass of the body, which is defined in the next section. Suffice to say here that the trajectories of O are the translational trajectories Tr and Tr of the body. The positions O and P at three different instants of time are shown by O , O , and O , and P , P and P , respectively, in both Figs.
. (a) and (b) . As seen from Fig. .
(a), at any instant the velocities of any particles like O and P of the body are the same in pure translation. Notice, in this case the orientation of OP, i.e. the angle OP makes with a fixed direction, say the horizontal, remains the same, i.e. α = α = α .
Fig. . (b) illustrates a case of combination of translation and rotation. In this case, at any instants the velocities of O and P differ.
Also, α , α and α may all be different. particles. The centre of mass of the system is that point C which is at a distance X from O, where X is given by X ( . ) In Eq.
( . ), X can be regarded as the mass- weighted mean of x and x . If the two particles have the same mass m = m = m , then mx mx X Thus, for two particles of equal mass the centre of mass lies exactly midway between them. If we have n particles of masses m , m , ...
m n respectively, along a straight line taken as the x - axis, then by definition the position of the centre of the mass