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Mechanics

Physics

$straight A space recording space disc space rotates space steadily space at space 45 space rev divided by min space on space straight a space table. space When space straight a space small space mass space of space 0.02 space kg space is space dropped space gently space on space the space disc space at space straight a space distance space of space 0.04 space straight m space from space its space axis space and space stucks space to space the space disc comma space the space rate space of space revolution space falls space to space 36 space rev divided by min. space The space moment space of space inertia space of space the space disc space about space its space centre space is$

$straight A space recording space disc space rotates space steadily space at space 45 space rev divided by min space on space straight a space table. space When space straight a space small space mass space of space 0.02 space kg space is space dropped space gently space on space the space disc space at space straight a space distance space of space 0.04 space straight m space from space its space axis space and space stucks space to space the space disc comma space the space rate space of space revolution space falls space to space 36 space rev divided by min. space The space moment space of space inertia space of space the space disc space about space its space centre space is$

PhysicsMechanics

Mechanics

Physics

Three identical masses. each of mass 1kg. are placed at the corners of an equilateral triangle of side l. Then the moment of inertia of this system about an axis along one side of the triangle is

Three identical masses. each of mass 1kg. are placed at the corners of an equilateral triangle of side l. Then the moment of inertia of this system about an axis along one side of the triangle is

PhysicsMechanics

Mechanics

Physics

The moment of inertia of a solid sphere about an axis passing through its centre is 0.8kgm² . The moment of inertia of another solid sphere whose mass is same as mass of first sphere. but the density is 8 times density of first sphere. about an axis passing through its centre is

The moment of inertia of a solid sphere about an axis passing through its centre is 0.8kgm² . The moment of inertia of another solid sphere whose mass is same as mass of first sphere. but the density is 8 times density of first sphere. about an axis passing through its centre is

PhysicsMechanics

Mechanics

Physics

The ratio of moments of inertia of a solid sphere about axes passing through its centre and tangent respectively is

The ratio of moments of inertia of a solid sphere about axes passing through its centre and tangent respectively is

PhysicsMechanics

Mechanics

Physics

$straight A space circular space platform space is space mounted space on space straight a space vertical space frictionless space axle. space Its space radius space straight r space equals space 2 straight m space and space its space moment space of space inertia space I italic space equals space 200 kg minus straight m squared space.. space It space is space initially space at space rest. space straight A space 70 space kg space man space stands space on space the space edge space of space the space platform space and space begins space to space walk space along space the space edge space at space speed space straight v subscript 0 space equals space 10 space straight m divided by straight s space relative space to space the space ground. space The space angular space velocity space of space the space platform space is space space space$

$straight A space circular space platform space is space mounted space on space straight a space vertical space frictionless space axle. space Its space radius space straight r space equals space 2 straight m space and space its space moment space of space inertia space I italic space equals space 200 kg minus straight m squared space.. space It space is space initially space at space rest. space straight A space 70 space kg space man space stands space on space the space edge space of space the space platform space and space begins space to space walk space along space the space edge space at space speed space straight v subscript 0 space equals space 10 space straight m divided by straight s space relative space to space the space ground. space The space angular space velocity space of space the space platform space is space space space$

PhysicsMechanics

Mechanics

Physics

$straight A space gramophone space record space has space radius space straight r space and space mass space straight M. space It space is space rotating space with space straight a space speed space omega. space Two space drops space of space wax space each space of space mass space straight m space fall space space on space it space at space straight a space distance space straight r divided by 2 space on space opposite space sides. space The space new space velocity space is space$

$straight A space gramophone space record space has space radius space straight r space and space mass space straight M. space It space is space rotating space with space straight a space speed space omega. space Two space drops space of space wax space each space of space mass space straight m space fall space space on space it space at space straight a space distance space straight r divided by 2 space on space opposite space sides. space The space new space velocity space is space$

PhysicsMechanics

Mechanics

Physics

$Angular space momentum space of space the space particle space rotating space with space straight a space central space force space is space constant space due space to space minus space space$

$Angular space momentum space of space the space particle space rotating space with space straight a space central space force space is space constant space due space to space minus space space$

PhysicsMechanics

Mechanics

Physics

$The space highest space moment space of space inertia space if space all space the space objects space have space same space mass space and space same space radius space is space of space minus$

$The space highest space moment space of space inertia space if space all space the space objects space have space same space mass space and space same space radius space is space of space minus$

PhysicsMechanics

Mechanics

Physics

$When space straight a space mass space is space rotated space in space straight a space plane space about space is space fixed space point comma space its space angular space momentum space is space directed space along space the minus$

$When space straight a space mass space is space rotated space in space straight a space plane space about space is space fixed space point comma space its space angular space momentum space is space directed space along space the minus$

PhysicsMechanics

Mechanics

Physics

$straight A space force space straight F with rightwards arrow on top equals straight a straight i with hat on top plus 3 straight j with hat on top plus 6 straight k with hat on top space is space acting space at space straight a space point space straight r with rightwards arrow on top equals 2 straight i with hat on top minus 6 straight j with hat on top minus 12 straight k with hat on top space The space value space of space apostrophe straight a apostrophe space for space which space angular space momentum space is space conserved space is space minus space$

$straight A space force space straight F with rightwards arrow on top equals straight a straight i with hat on top plus 3 straight j with hat on top plus 6 straight k with hat on top space is space acting space at space straight a space point space straight r with rightwards arrow on top equals 2 straight i with hat on top minus 6 straight j with hat on top minus 12 straight k with hat on top space The space value space of space apostrophe straight a apostrophe space for space which space angular space momentum space is space conserved space is space minus space$

PhysicsMechanics

Mechanics

Physics

Thickness of a wooden circular plate is same as the thickness of a metal circular plate but density of metal plate is 8 times density of wooden plate. If moment of inertia of wooden plate is twice the moment of inertia of metal plate about their natural axes, then the ratio of radii of wooden plate to metal plate is

Thickness of a wooden circular plate is same as the thickness of a metal circular plate but density of metal plate is 8 times density of wooden plate. If moment of inertia of wooden plate is twice the moment of inertia of metal plate about their natural axes, then the ratio of radii of wooden plate to metal plate is

PhysicsMechanics

Mechanics

Physics

$straight A space particle space performs space uniform space circular space motion space with space angular space momentum space apostrophe straight L apostrophe. space If space the space frequency space of space particles space motion space is space halved space and space its space KE space is space doubled space then space the space angular space momentum space becomes space$

$straight A space particle space performs space uniform space circular space motion space with space angular space momentum space apostrophe straight L apostrophe. space If space the space frequency space of space particles space motion space is space halved space and space its space KE space is space doubled space then space the space angular space momentum space becomes space$

PhysicsMechanics

Mechanics

Physics

$straight A space particle space is space moved space in space straight a space circle space with space straight a space constant space angular space velocity. space Its space angular space momentum space is space straight L. space If space the space radius space of space the space circle space is space halved space keeping space the space angular space velocity space same comma space the space angular space momentum space of space the space particle space will space become space minus$

$straight A space particle space is space moved space in space straight a space circle space with space straight a space constant space angular space velocity. space Its space angular space momentum space is space straight L. space If space the space radius space of space the space circle space is space halved space keeping space the space angular space velocity space same comma space the space angular space momentum space of space the space particle space will space become space minus$

PhysicsMechanics

Mechanics

Physics

$straight A space smooth space tube space of space certain space mass space is space rotated space in space straight a space gravity minus free space space space and space released. space The space two space balls space shown space in space Fig. space move space towards space the space ends space of space the space tube. space For space the space whole space system comma space which space of space the space following space quantities space is space not space conserved.$

$straight A space smooth space tube space of space certain space mass space is space rotated space in space straight a space gravity minus free space space space and space released. space The space two space balls space shown space in space Fig. space move space towards space the space ends space of space the space tube. space For space the space whole space system comma space which space of space the space following space quantities space is space not space conserved.$

PhysicsMechanics

Mechanics

Physics

$straight A space thin space uniform space rod space of space mass space straight m space and space length space l space is space kept space on space straight a space smooth space horizontal space surface space such space that space it space can space move space freely. space At space what space distance space from space centre space of space rod space should space straight a space particle space of space mass space straight m space strike space on the space rod space such space that space the space point space straight P space at space straight a space distance italic space l italic divided by italic 3 space from space the space end space of space the space rod space is space instantaneously space at space rest space just space after space the space elastic space collision ? space$

$straight A space thin space uniform space rod space of space mass space straight m space and space length space l space is space kept space on space straight a space smooth space horizontal space surface space such space that space it space can space move space freely. space At space what space distance space from space centre space of space rod space should space straight a space particle space of space mass space straight m space strike space on the space rod space such space that space the space point space straight P space at space straight a space distance italic space l italic divided by italic 3 space from space the space end space of space the space rod space is space instantaneously space at space rest space just space after space the space elastic space collision ? space$

PhysicsMechanics

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