Author: Physics Notebook
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Derive An Expression For The Angular Momentum Of A Rigid Body.
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Angular momentum: Let us consider a rigid body rotates with angular velocity about a fixed point O which is taken as origin . OX, OY and OZ are the three mutually perpendicular axes. , where , and are the components along OX, OY and OZ axes respectively. Let be the position vector of the ith…
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Consider The Motion Of Two Masses m1 and m2. Calculate The Kinetic Energy Of The Particles In The Centre Of Mass Frame Of Reference.
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Ans. Let us consider a system of two masses and having position vectors and respectively with respect to the origin O. If be the position vector of the centre of mass C of the system then . Let, and be the position vectors of the masses and with respect to the centre of mass C.…
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Reduce Two Body Problem Into One Body Problem And Obtain Equation Of Motion For Equivalent One Body Problem For Two Masses.
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Ans. Let us consider a system of two masses and having position vectors and respectively with respect to the origin O. If be the position vector of the centre of mass C of the system with respect to the origin O, then Let the two masses and are separated by a distance and acted upon…
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Two Particles Of Masses m1 And m2 Have A Relative Motion. Under What Condition Does Their Centre Of Mass Remains Stationary?
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Ans. Let us consider two particles of masses and having position vectors and respectively with respect to the origin O, have a relative motion between them. Their centre of mass lies on the line joining them. So the force on due to the mass and the force on due to the mas are both directed…
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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.
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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 that the angular momentum or, or, or, or, or, or, or, , since is constant.
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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.
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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 system is given by, or, or, So the co-ordinate of the centre of mass of the system is (2,0,2)
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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.
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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 respect to the origin O. Therefore, or, or, or, or, where, and are the velocities of the masses and respectively and is the velocity of…
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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.
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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 centre of mass C of this system having position vector is given by If the centre of mass lies at the origin O of the…
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What Is Angular Impulse Of A System Of Particles?
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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 that , [ to know the derivation (CLICK HERE) ] If and be the total angular momenta of the system at times and respectively, then…
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What Is Linear Impulse Of A System Of Particles?
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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 in linear momentum. If be the total mass of he system and be the velocity of the centre of mass of the system then we…