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Physics

Mechanics

Easy

Question

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

$constant torque$
$constant force$
$constant linear momentum$
$zero torque$

The correct answer is: $zero space torque space space$

$Sol colon space space space Torque space of space central space force space straight w. straight r. straight t. space CM space is space zero space space space colon space Angular space momentum space is space constant space space space space space space space space$

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

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

PhysicsMechanics

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

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

PhysicsMechanics

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

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

PhysicsMechanics

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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

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

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

PhysicsMechanics

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

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

PhysicsMechanics

parallel

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

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

PhysicsMechanics

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

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

PhysicsMechanics

$straight A space cube space of space side space straight a space and space mass space straight m space is space to space be space tilted space at space point space straight A space by space applying space straight a space force space straight F space as space shown space in space Fig. space The space minimum space force space required space is$

$straight A space cube space of space side space straight a space and space mass space straight m space is space to space be space tilted space at space point space straight A space by space applying space straight a space force space straight F space as space shown space in space Fig. space The space minimum space force space required space is$

PhysicsMechanics

parallel

$Three space point space masses space straight m subscript 1 space comma straight m subscript 2 space and space space straight m subscript 3 space are space located space at space the space vertices space of space an space equilateral space triangle space of space side space apostrophe space straight a apostrophe space. space What space is space the space moment space of space inertia space of space the space system space about space an space axis space along space the space altitude space of space the space triangle space passing space through space straight m subscript 1 space space ?$

$Three space point space masses space straight m subscript 1 space comma straight m subscript 2 space and space space straight m subscript 3 space are space located space at space the space vertices space of space an space equilateral space triangle space of space side space apostrophe space straight a apostrophe space. space What space is space the space moment space of space inertia space of space the space system space about space an space axis space along space the space altitude space of space the space triangle space passing space through space straight m subscript 1 space space ?$

PhysicsMechanics

$straight A space uniformthin space rod space of space length italic space l italic space and space mass space straight m space is space hinged space at space straight a space distance italic space l italic divided by italic 4 space space from space one space of space the space end space and space released space from space horizontal space position space as space shown space in space Fig. The space angular space velocity space of space the space rod space as space it space passes the space vertical space position space is$

$straight A space uniformthin space rod space of space length italic space l italic space and space mass space straight m space is space hinged space at space straight a space distance italic space l italic divided by italic 4 space space from space one space of space the space end space and space released space from space horizontal space position space as space shown space in space Fig. The space angular space velocity space of space the space rod space as space it space passes the space vertical space position space is$

PhysicsMechanics

$straight A space uniform space disc space of space mass space straight M space and space radius space straight R space is space mounted space on space an space axle space supported space in space frictionless space bearings. space straight A space light space cord space is space wrapped space around space the space rim space of space the space disc space and space straight a space steady space downward space pull space straight T space is space exerted space on space the space cord. space The space angular space acceleration space of space the space disc space is$

$straight A space uniform space disc space of space mass space straight M space and space radius space straight R space is space mounted space on space an space axle space supported space in space frictionless space bearings. space straight A space light space cord space is space wrapped space around space the space rim space of space the space disc space and space straight a space steady space downward space pull space straight T space is space exerted space on space the space cord. space The space angular space acceleration space of space the space disc space is$

PhysicsMechanics

parallel

$Two space rings space of space same space radius space and space mass space are space placed space such space that space their space centres space are space at space straight a space space common space point space and space their space planes space are space perpendicular space to space each space other. space The space moment space of space inertia space of space the space system space about space an space axis space passing space through space the space centre space and space perpendicular space to space the space plane space of space one space of space the space rings space is space left parenthesis mass space of space the space ring space equals space straight m comma space radius space equals space straight r right parenthesis$

$Two space rings space of space same space radius space and space mass space are space placed space such space that space their space centres space are space at space straight a space space common space point space and space their space planes space are space perpendicular space to space each space other. space The space moment space of space inertia space of space the space system space about space an space axis space passing space through space the space centre space and space perpendicular space to space the space plane space of space one space of space the space rings space is space left parenthesis mass space of space the space ring space equals space straight m comma space radius space equals space straight r right parenthesis$

PhysicsMechanics

Seven identical disc are arranged in a hexagonal, planar pattern so as to touch each neighbour, as shown in the figure. Each disc has mass m and radius r. What is the moment of inertia of the system of seven disks about an axis passing through the centre of central disk and normal to plane of all disks?

Seven identical disc are arranged in a hexagonal, planar pattern so as to touch each neighbour, as shown in the figure. Each disc has mass m and radius r. What is the moment of inertia of the system of seven disks about an axis passing through the centre of central disk and normal to plane of all disks?

PhysicsMechanics

A solid aluminium sphere of radius R has moment of inertia I about an axis through its centre. The moment of inertia about a central axis of a solid aluminium sphere of radius 2R is

A solid aluminium sphere of radius R has moment of inertia I about an axis through its centre. The moment of inertia about a central axis of a solid aluminium sphere of radius 2R is

PhysicsMechanics

parallel

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