Separation of mmotion of a systme of particles into motion of the centre of mass and motion about the centre of mass
Show `vecp = vec p_i + m_i vecV` where `vecp_i` is the momentum of the ith particle

Separation of mmotion of a systme of particles into motion of the centre of mass and motion about the centre of mass Show K = K + 1/2 MV^2 , where k is the total kinetic energy of the system of particles, K is the total kinetic energy of the system when the particle velcoities are taken with respect to the centre of mass and MV^2//2 is the kinetic energy of the translation of the system as a whole (i,e of the centre of mass motion of the system).

Separation of mmotion of a systme of particles into motion of the centre of mass and motion about the centre of mass Show vec L = L = vec L + vecM R xx vecV where vec L = Sigma vecr_i xx vecp_i is the angular momentum of the system about the centre of mass with velocities taken relative to the centre of mass. Remember vecr_i = vecr_i - vecR , rest f the notation is the standard notation used in the chapter. Note vecL and vecMR xx vecV can be said to be angular moemnta respectively about and of the centre of mass of the system of particles.

Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass :- Show (dL')/(dt)=(sumr_i') xx (dp')/(dt) Further, show that (dL')/(dt)= tau'_(ext) where tau'_(ext) is the sum of all external torques acting on the system about the centre of mass.

One end of a string of length t is connected to a particle of mass m and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed v the net force on the particle (directed towards the centre) is : T is the tension in the string. [Choose the correct alternative].

Consider a two - particle system with the particles having masses M_1 and M_2 .If the first particle is pushed towards the centre of mass through a distance a,by what distance whould the second particle be moved,so as t keep the centre of mass at the same position?

A paticle of mass m is executing uniform circular motion on a path of radius r. If p is the magnitude of its linear momentum, then the radial force acting on the particle is

Discuss the motion of a charged particle in uniform magnetic field, when it moves at an angle 0 with the direction of magnetic field. Prove that its path is helical.Calculate the pitch of the helical path.What will be the nature of the path, if (i) theta = 0^@ and (ii) theta = 180^@ ?