Angular Momentum & Centre Of Mass
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Show That Total Linear Momentum Of A System Of Particles About The Centre Of Mass Is Zero.
Total linear momentum about the centre of mass: Let us consider a system of n particles of masses , , having position vectors , , , respectively with respect to…
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Show That The Total Linear Momentum Of A System Of Particles Is Equal To The Linear Momentum Of The Centre Of Mass.
Linear momentum of a system of particles: The position vector of the centre of mass of a system of n particles relative to the origin O is given by, where,…
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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. Let us consider a system of n particles of masses , , , having position vector , , , with respect to the origin O. Let P be the…
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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. Let us consider a system of n particles of masses , , , having position vector , , , with respect to the origin O. Let P be the…
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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. Let us consider a system of n particles of masses , , , having position vector , , , with respect to the origin O. If be the position…
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Define Angular Momentum For A System Of Particles.
Angular momentum for a system of particles: Let us consider a system of n particles of masses , , , having position vectors , , , respectively with respect to…
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Define Total External Torque Acting On A System Of Particles.
Total external torque acting on a system of particles: If be the external force acting on ith particle of mass having position vector with respect to the origin, then the…
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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…