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Define Angular Momentum Of A Particle And Torque Acting On It.
Angular Momentum: The angular momentum of a particle about a fixed point is defined by the moment of linear momentum of the particle about that fixed point. If be the position vector of a particle of mass with respect to the fixed point O and be the linear momentum of that particle then, the angular…
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Show That The Torque Acting On A Particle Is Equal To The Time Rate Of Change Of Its Angular Momentum.
Ans. The angular momentum of a particle is given by, where is the linear momentum of a particle of mass m whose position vector with respect to the origin of a inertial reference frame is . If be the velocity of the particle then, and Differentiating both side pf equation (1) with respect to time,…
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State And Prove The Law Of Conservation Of Angular Momentum.
Law of conservation of angular momentum: If the total external torque acting on a particle is zero, then the angular momentum remains conserved. This is known as the law of conservation of angular momentum. We know that the time rate of change of angular momentum of a particle is equal to the torque acting on…
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What Do You Mean By Angular Impulse?
Angular Impulse: The product of torque acting on a particle and the time during which it acts, is called angular impulse. If an external torque acts on a particle during the time from to , then the angular impulse is
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Show That Angular Impulse Is Equal To The Change Of Angular Momentum.
If an external torque acts on a particle during the time from to , then the angular impulse is given by, Again we know that the torque acting on a particle is equal to the time rate of change of linear momentum of that particle, So [ To know the derivation (CLICK HERE) ] Let…
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Define Centre Of Mass.
Centre of mass: Let us consider a system of n particles of masses m1, m2, …. mn with position vectors , , , respectively with respect to the origin O, as shown in the above Fig. 1. The centre of mass of the system is defined as the point with position vector , is given…
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Derive The Velocity And Acceleration Of Centre Of Mass.
Velocity of centre of mass: For a system of n particles of masses , , , having position vectors , , , respectively with respect to the origin O, the centre of mass is defined by the point having position vector given by, [Where is the total mass of the system.] or, or, Differentiating both…
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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: 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,…
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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 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…
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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, 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…
