Author: Physics Notebook
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Prove That The Total Momentum Of A System Is Constant i.e., Conserved Then The Centre Of Mass Is Either At Rest Or In Motion With Constant Velocity.
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Ans. Let us consider be the position vector of ith particle of a system of n particles with respect to the origin and be the velocity of that ith particle of mass . So the momentum of the system is given by, where, is the position vector of the centre of mass of the system…
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Prove That The Centre Of Mass Of A System Of Particles Moves As If The Total Mass And The Resultant External Force Were Applied At This Point.
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Let us consider be the resultant external force acting on the ith particle of a system of n particles and be the internal force on the ith particle due to the jth particle. So the resultant internal force on the ith particle due to all other particle is , where . If be the linear…
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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).
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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 internal force on the ith particle due to the jth particle. So the resultant internal force on the ith particle due to all other particle…
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Define Total External Torque Acting On A System Of Particles.
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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 moment of force or torque about that origin is . So the total external torque acting on a system of n particles is given by,
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Define Angular Momentum For A System Of Particles.
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Angular momentum for a system of particles: Let us consider a system of n particles of masses , , , having position vectors , , , respectively with respect to the origin O, whose velocities are , , , respectively. So the angular momentum of the system about the origin O is given by, or,…
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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.
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Ans. Let us consider a system of n particles of masses , , , having position vector , , , with respect to the origin O. If be the position vector with respect to the origin O of the ith particle of mass and be the velocity of that its particle, then the total kinetic…
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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.
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Ans. Let us consider a system of n particles of masses , , , having position vector , , , with respect to the origin O. Let P be the centre of mass of the system having position vector with respect to the origin O is given by, where, is the position vector of the…
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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.
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Ans. Let us consider a system of n particles of masses , , , having position vector , , , with respect to the origin O. Let P be the centre of mass of the system having position vector with respect to the origin O is given by, where, is the position vector of the…
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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.
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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, is the position vector of the its particle of mass with respect to the origin O, is the total mass of the system of n…
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Show That Total Linear Momentum Of A System Of Particles About The Centre Of Mass Is Zero.
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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 the origin O as shown in the above Fig. 1. Let P be the centre of mass of the system of n particle, with position…