Prove That The Total External Torque Acting On A System Of Particles Is Equal To The Time Rate Of Angular Momentum Of The System, Provided That The Internal Forces Between The Particles Are Central Forces (i.e., The Internal Forces Between Any Two Particles Are Always Directed Along The Line Joining The Particles).

Relation between angular momentum and total external torque: Let us consider be the resultant external force acting on the ith particle of a system of n particles and be the…

Continue ReadingProve That The Total External Torque Acting On A System Of Particles Is Equal To The Time Rate Of Angular Momentum Of The System, Provided That The Internal Forces Between The Particles Are Central Forces (i.e., The Internal Forces Between Any Two Particles Are Always Directed Along The Line Joining The Particles).

Prove That The Total Kinetic Energy Of A System Of Particles About Any Point Is Equal To The Kinetic Energy Of The Centre Of Mass Plus The Kinetic Energy Of Motion About The Centre Of Mass.

Ans. Fig. 1 Let us consider a system of n particles of masses , , , having position vector , , , with respect to the origin O. If be…

Continue ReadingProve That The Total Kinetic Energy Of A System Of Particles About Any Point Is Equal To The Kinetic Energy Of The Centre Of Mass Plus The Kinetic Energy Of Motion About The Centre Of Mass.

A Number Of Particles Collide With One Another, If No External Force Acts On Them, Find The Angular Momentum Relative To the Coordinate System With Centre Of Mass At The Origin.

Ans. Fig. 1 Let us consider a system of n particles of masses , , , having position vector , , , with respect to the origin O. Let P…

Continue ReadingA Number Of Particles Collide With One Another, If No External Force Acts On Them, Find The Angular Momentum Relative To the Coordinate System With Centre Of Mass At The Origin.

Prove That The Total Angular Momentum Of A System Of Particles About Any Point O Is Equal To The Angular Momentum Of The Total Mass Assumed To Be Located At The Centre Of Mass.

Ans. Fig. 1 Let us consider a system of n particles of masses , , , having position vector , , , with respect to the origin O. Let P…

Continue ReadingProve That The Total Angular Momentum Of A System Of Particles About Any Point O Is Equal To The Angular Momentum Of The Total Mass Assumed To Be Located At The Centre Of Mass.

Show That The Sum Of The Products Of Mass And Position Vectors Of All Particles i.e., The Sum Of Moments Of Mass Points About The Centre Of Mass Is Zero.

The total moment of mass about the centre of mass: Fig. 1 Let us consider a system of n particles of masses , , having position vectors , , ,…

Continue ReadingShow That The Sum Of The Products Of Mass And Position Vectors Of All Particles i.e., The Sum Of Moments Of Mass Points About The Centre Of Mass Is Zero.