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Mechanics

Physics

$straight A space uniform space rod space of space mass space straight M equals 2 kg space and space length space straight L space is space suspended space by space two space smooth space hinges space 1 space and space 2 space as space shown space in space figure. space straight A space force space straight F equals 4 straight N space is space applied space downward space at space straight a space distance space straight L divided by 4 space from space hinge space 2. space Due space to space the space application space of space force space straight F comma space hinge space 2 space breaks. space At space this space instant space comma space applied space force space straight F space is space also space removed. space The space rod space starts space to space rotate space downward space about space hinge space 1. space open italic left parenthesis g equals 10 m divided by s squared close parentheses$
$The space reaction space at space hinge space 1 comma space before space space hinge space 2 space breaks comma space is space$

$straight A space uniform space rod space of space mass space straight M equals 2 kg space and space length space straight L space is space suspended space by space two space smooth space hinges space 1 space and space 2 space as space shown space in space figure. space straight A space force space straight F equals 4 straight N space is space applied space downward space at space straight a space distance space straight L divided by 4 space from space hinge space 2. space Due space to space the space application space of space force space straight F comma space hinge space 2 space breaks. space At space this space instant space comma space applied space force space straight F space is space also space removed. space The space rod space starts space to space rotate space downward space about space hinge space 1. space open italic left parenthesis g equals 10 m divided by s squared close parentheses$
$The space reaction space at space hinge space 1 comma space before space space hinge space 2 space breaks comma space is space$

PhysicsMechanics

Mechanics

Physics

$The space horizontal space beam space in space figure space weighs space 150 straight N comma space and space its space centre space of space gravity space is space at space its space centre. space Find space$

The horizontal and vertical components of the force exerted on the beam at the wall

$The space horizontal space beam space in space figure space weighs space 150 straight N comma space and space its space centre space of space gravity space is space at space its space centre. space Find space$

The horizontal and vertical components of the force exerted on the beam at the wall

PhysicsMechanics

Mechanics

Physics

$The space horizontal space beam space in space figure space weighs space 150 straight N comma space and space its space centre space of space gravity space is space at space its space centre. space Find space$

The tension in the cable

$The space horizontal space beam space in space figure space weighs space 150 straight N comma space and space its space centre space of space gravity space is space at space its space centre. space Find space$

The tension in the cable

PhysicsMechanics

Mechanics

Physics

$Four space spheres space of space diameter space 2 straight a space and space mass space straight M space are space placed space with space their space centres space on space the space four space corners space of space straight a space square space of space side space straight b. space Then space the space moment space of space Inertia space of space the space system space about space an space axis space along space one space of space the space sides space of space the space square space is space$

$Four space spheres space of space diameter space 2 straight a space and space mass space straight M space are space placed space with space their space centres space on space the space four space corners space of space straight a space square space of space side space straight b. space Then space the space moment space of space Inertia space of space the space system space about space an space axis space along space one space of space the space sides space of space the space square space is space$

PhysicsMechanics

Mechanics

Physics

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

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

PhysicsMechanics

Mechanics

Physics

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

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

PhysicsMechanics

Mechanics

Physics

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

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

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

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

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

PhysicsMechanics

Mechanics

Physics

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

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

PhysicsMechanics

Mechanics

Physics

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

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

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

The minimum height of the obstacle so that the sphere can stay in equilibrium is (R is radius of the sphere)

The minimum height of the obstacle so that the sphere can stay in equilibrium is (R is radius of the sphere)

PhysicsMechanics

Mechanics

Physics

$A space c y l i n d e r space r e s t s space o n space a space h o r i z o n t a l space r o t a t i n g space d i s c space a s space s h o w n. space D i s tan c e space b e t w e e n space t h e space a x e s space o f space t h e space d i s c space text and cylinder is end text straight R text . Coefficient of friction between disc and cylinder is end text mu greater than D over h. text Where end text D equals 2 r text is end text text diameter of cylinder. Value of end text omega text such that cylinder falls off the disc will be end text$

$A space c y l i n d e r space r e s t s space o n space a space h o r i z o n t a l space r o t a t i n g space d i s c space a s space s h o w n. space D i s tan c e space b e t w e e n space t h e space a x e s space o f space t h e space d i s c space text and cylinder is end text straight R text . Coefficient of friction between disc and cylinder is end text mu greater than D over h. text Where end text D equals 2 r text is end text text diameter of cylinder. Value of end text omega text such that cylinder falls off the disc will be end text$

PhysicsMechanics

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