Angular Momentum & Centre Of Mass
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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.
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…
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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.
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…
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What Is Linear Impulse Of A System Of Particles?
Linear impulse: If be the total external force acting on a system of particles, then the total linear impulse will be . This linear impulse is equal to the change…
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What Is Angular Impulse Of A System Of Particles?
Angular impulse: If be the total external torque applied to a system of particles about the origin, then the total angular impulse of the system will be . We know…
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Show That Centre Of Mass Of Two Particles System Divides The Line Joining The Two Particles In The Inverse Ratio Of Their Masses.
Ans. Let us consider a system of two particles of masses and having position vectors and respectively with respect to the origin O as shown in the Fig. 1. The…
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Two Particles Having Masses “m1” And “m2” Move So That Their Relative Velocity is “v” And The Velocity Of Their Centre Of Mass Is “V”. Calculate The Total Potential Energy.
Ans. Let us consider two particles of masses and having position vector and with respect to the origin O. Let be the position vector of centre of mass C with…
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A Quadrilateral ABCD Has Masses 1,2,3 And 4 Units Located At Its Vertices A(-1,-2,2), B(3,2,-1), C(1,-2,4) And D(3,1,2). Find The Coordinate Of The Centre Of Mass.
Ans. Position vector of A is Position vector of B is Position vector of C is and Position vector of D is . So the centre of mass of the…
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A Particle Is Moving In A Circular Orbit Of Radius “r” With A Speed “V”. Show That The Curl Of “V” is Equal To 2ω, Where ω Is The Angular Velocity Of The Particle. Also Show That The Angular Momentum Is Conserved.
Ans. Let us consider the position vector of the particle is given by, and the angular velocity of that particle is given by, Therefore, now and, Therefore, Again we know…