Title 04. (A) CENTRE OF MASS.pdf ✅

1 CENTER OF MASS Total Sessions – 06 SESSION – 1 AIM ✓ To introduce concept of Centre of Mass ✓ Centre of mass of system of particles a) Position of Centre of Mass: System of two particles b) Position of Centre of Mass: System of multiple particles THEORY CENTRE OF MASS The center of mass of an object is the point associated with the system that moves in the same way as a point mass having mass equal to the object would move when subjected to the same external forces that act on the object. Therefore the motion of system can be observed as motion of center of mass alone. ➢ The CM of a body (or system of particles) is defined as a point at which the entire mass of the body is supposed to be concentrated. ➢ When an object moves, it moves in the same way as a point mass of same mass equal to the object would move. ➢ All the particles move about the centre of mass in different directions but follows the CM. ➢ Any external force acting on the object will be as if it is acting on Centre of Mass and the object will move with the acceleration of CM. ➢ Position of CM may lie within or outside the material of the body. POSITION OF CENTRE OF MASS a] System of two particle: Consider first a system of two particles m1 and m2 at distances x1 and x2 respectively, from some origin O. We define a point C, the center of mass of the system, as a distance xcm from the origin O, where xcm is defined by xcm = m1x1+m2x2 m1+m2 Es..... of M of Mass about the CM = 0 m1 (−r1 ) + m2 (r2 ) = 0 m1r1 = m2r2 m1 (xc − x1 ) = m2 (x2 − xc ) m1xc − m1x1 = m2x2 − m2xc (m1 + m2 )xc = m1x1 + m2x2 xc = m1x1+m2x2 m1+m2 . . (x , 0) 1 (x , 0) cm (x , 0) 2 m1 m2