ROTATIONAL DYNAMICS | MHT-CET PYQ 2022 PHYSICS | MHT CET 2023 | IMPULSE BATCH

uh good morning students rotational Dynamics analysis okay majority of questions foreign particle of mass 10 gram okay Mass delay 10 gram 10 grams so 10 to the power minus 2 kg 10 to the power minus 2 kg okay put it radius 6.4 centimeter means 10 to the power minus 2 meter okay tangential acceleration Act of the particles the particles of velocity kinetic energy of particle becomes by the end of Second Revolution kinetic energy because of financial acceleration half MV Square is equal to 8 into 10 to the power minus 4 EOD kinetic energy is simple mass divided 10 raised to minus 2. minus 4 and equality minus two minus 10 raise to minus 2 will work his own 0.4 foreign 2 into acceleration tangential shoulder is foreign foreign six into three is twenty twenty Jasper's product answer so 2 divided by Twenty apply acceleration so maladri has 0.1 as a calculation okay uh maybe throw us a problem acceleration but unit velocities okay so velocity is up on 0.4 meter per second correct so those system will answer it acceleration is possible uh even actual MST City uh uniform Rod a b of mass m and length l okay but okay is at rest on this smooth horizontal surface surface and impulse p is applied to the end B Anana impulse is a large amount of force applied for a small duration short duration Force into the durations into acceleration acceleration was a velocity by time cancel so basically impulse apply kill any momentum is nothing but momentum actually okay momentum then time taken by the rod to turn through right angle momentum actually a linear momentum yeah about foreign gold filter correct 90 degrees okay that is equal to p p m v so how's the momentum angular momentum an angular momentum is linear momentum that is MV into the distance from the axis of rotation L by two velocity angle of velocity so p l divided by 2 is equal to IH value moment of inertia value m l Square divided by 12 tax is about into Omega so 6 into p in 6 into P divided by ml Omega the angular velocity uh six P divided by ml a angle is per second Omega unit is radian per second so everyday Radiance okay it's a pi by 2 radians cross multiplication correct so 6 P divided by ml it should be equal to okay 6p divided by ml into that question mark it should be equal to it should be equal to okay uh Pi by 2 into 1. foreign acceleration speed is doubled and the ratio of its acceleration after and before is remember acceleration is a Formula V Square by r month particle is moving along a circular path with the constant speed and centripetal acceleration 8 centripetal acceleration AI speed double kilometers okay then the ratio of acceleration after after all acceleration 4 times before Vala acceleration one Diamond so four is to a national answer is foreign uh next question question number four a solid sphere of mass m and radius r its moment of inertia about parallel axis passing through a point at a distance R by 2 from the center again so early disappears the moment of inertia about diameter is two by five m r Square plus axis so R by 2 distance R by two distance everything foreign MH Square K 1 2 by 5 m r Square Plus m r Square divided by 4. T So M R square is okay plus uh one by four cross multiplication eight plus five is thirteen by Twenty thirteen by Twenty Mr Square okay Apple answer question number question number five actually misplayz okay next question ah two circular Loops p and Q okay don't circular Loop uh okay moment of inertia of Q okay moment of inertia about its axis is 4 times out of P of Q okay m r Square m r Square by 2 ring okay m r Square other moment of inertia ha is four times that of moment of inertia of this ring of the carrying some amount of inertia mass of ring p into R square correct it's like relation to one of it is foreign okay actually n times Pizza Mass hello okay linear mass density of Sigma linear Mass densities so 2 pi r Yoda meter law Sigma into two kilometer mass is proportional to radius that's the radius circumference simple radius is a mass cancel correct so n into this n Square n Cube into R square should be equal to 4 into R square R square R square cancels so n Cube half foreign correct option number B next question question number seven okay a thin metal rod of mass m and length L is cut into four equal parts like metal product okay okay a moment of energy of Rod about axis passing through its Center and perpendicular to axis about same axis foreign by 12. correctly moment of inertia is okay into L Square by 16 . 1 by 64 times amount of inertia one divided by what 64 times inertia question number eight so it is a magnetic field question is charge moves in a circular path perpendicular to its magnetic magnetic field [Music] um this output magnetic field other charge okay foreign force acting on a charge moving in a magnetic field okay shortness okay so Q into V into b q v b sine Theta but it's a velocity any field here perpendicular foreign [Music] that means angular velocity does not depend on velocity angular velocity and just time period and the time period 2 pi by Omega Omega is so time period does not depend on velocity of the charge so charge worthy foreign foreign that is qvb a magnetic field is okay see question number nine question number nine mother uh okay uh the pi by two which is foreign correct so T cos theta plus per second 2 by pi Revolution with the two pyridiana per second cancel so Omega is a value for eign L cos Theta by G and time period 2 pi divided by Omega Omega 4 right 2 pi 2 pi cancels Allah 1 by 16 is equal to l cos Theta by G cos he does the value so there's a so G worth is that so G by 16 l a COS Theta value one though G by 16 l cancel 16 ml 16 ml that is option number eight so it has a mistake would be Pi by 2 another 2 by pi Hawaii okay but as it is a screenshots okay foreign foreign support foreign foreign foreign foreign foreign bro subscribe okay just after the impact while angular velocity okay uh M into V is the momentum linear momentum yeah angular momentum is M into V linear momentum into distance foreign Square by 3 foreign about this particular axis M into R square minus L Square um foreign so M into V into l is equal to l Square upon common group bracket uh M plus 3M divided by 3 into Omega Omega LL cancel three degrees on multiply so 3 MV 3 uh M into V T and the uh divided on our bracket mother M plus 3M options correct the next question number 11. uh road is 10 meter wide again 10 meter wide it's a radius of curvature is uh 50 meters there is a radius of curvature a 50 meter okay Outer Edge is uh above the inner Edge by a distance of 1.5 meter okay throws a banking lessons that is 10 meter even higher Dimension any hard I mentioned almost equalizer for small uh Capital elevation to you otherwise this road is most suited for the velocity banking off roads are formula um time Theta is equal to V Square by RG the derivation is into V Square by RG ATA time Theta is opposite side angle of banking opposite side which is 1.5 divided by adjacent side that is equal to 10. is equal to V square like velocity is a square divided by R into G radius 50 into G so 0 and it has 0 cancel uh okay nine point it is fine to 1.5 7.5 into G so V square is equal to V square is equal to 7.5 into G1 calculations directly 12th question a disk of mass 25 gram kilogram and radius 0.2 is rotating at 240 Revolution per minute okay retarding torque uh foreign is the angular velocity [Music] foreign angular velocity by time taken final velocity the zeros value initials divided ten seconds sorry twenty seconds a value okay so to these four four this is five uh Mr Square Pi Mr Square by 5. so torque is equal to Pi and mask it is 25 Pi m r Square 0.2 the square is 0.2 into again 0.2 divided by getting five tier 0.2 into point two is point zero four okay a point zero formal multiplication that how multiplication uh actually one mantra 0.04 by 100 cancel one month so tax value Pi by five ultimately so torque is equal to pi divided by five but towards the formula is to force into uh distance so that Force into this perpendicular distance from axis foreign performs uniform circular motion of radius r with a velocity V okay today uh if m v and R are increased by 50 so greater than 50 50 then the necessary change in force required to maintain the particle in the uniform circular motion is what centripetal force other which are that centripetal force or MV Square the mass 50 increase Horizon so must I give 1.5 mm velocity 50 increase 1.5 times put any velocity velocity radius fifty percent increase the radius so 1.5 1.5 cancels all AC at the 1.5 Square Anna so 2.251 so 2.25 into m into this V Square divided by Kali r plus centripetal force Adisa centripetal force 2.25 times correct either okay then the necessary change in force money change in force 2.25 times 2.25 MB Square bar and add these are centripetal force is like MV Square bar Square bar MV Square bar common question so 2.25 minus 1 is 1.25 so every centriple Force change is 125 percentage 125 percent when 25 means 125 divided by 100 is 1.25 1.25 times change okay otherwise percentage percentage change divided by original into hundred change GTA 1.25 MV Square bar original MV Square bar into 100 now cancel cancel 1.25 200 is 125. t so the next question number 14 question return uh basically like a table Magic okay the uh match the following columns Army radius maybe cable is the column two I guess the radius of directions okay okay k for solid sphere rotating about its tangent about solid sphere rotating about tangenta solid space m r Square moment of inertia actual moment of inertia of solid sphere rotating about tangent but radius of guys seven by five into r okay uh foreign but it's a match up XC another d well okay uh k for ring rotating about tangent perpendicular to its plane at the ring settings about moment of inertia is m r Square but tangent about perpendicular to its plane the reaction is Mr square plus MH Square H is again R so answer should be 2 m r Square propular radius of Correction radius of variation format there is root 2 times r so Visa match how root 2 times okay question number 15. car is driven on the bank load of radius of curvature 20 with a maximum safe speed okay in order to increase its safety speed by 10 percent you have a banking off-roads tan Theta is equal to V Square by RG car is driven on the bank Road of radius of curvature 20 meter okay with a maximum safe speed maximum safe speed manager however formula used Horizon okay don't like 10 millimeters upper speed limit lower speed limit and a maximum safe speed safest speed uh V square is equal to foreign into g into tan Theta in order to increase safety speed by 10 percent have a velocity safe speed okay and the safe speed had 10 percent speed is V V just 10 percent tomorrow then increase in radius of curvature will be what foreign foreign velocity is 1.1 times original velocity okay uh it is tomorrow 1.1 times 1.1 times correct yourself the right hand side 1.1 times basically have 1.1 times velocity 1.1 times value correct other 1.1 times 1.21 square root so radius should be 1.21 times original radius foreign of a ring to that of disk of same radius and same mass about tangent about tangential axis perpendicular to its plane never bring some amount of inertia about tangent it's about moment of inertia so M R square and H about Kitty parallel axis theorem plus MH square that means 2 m r Square so Rings the moment of inertia is to m r Square okay other disc 30. this amount of energy about this particular X is Mr Square by 2 plus accessed about COs plus m r Square by using parallel axis that is three by two m r Square okay the radius of directions the ratio of each other while the moment of inertia is um divided by moment of inertia of disc is equal to bring some amount of inertia is to m r Square this amount of inertia is three by two m r Square Mr square m r Square cancel a vertical of the four by three one another four by three literally as a ringing some moment of inertia is storing some Mass into radius of variations of square this amount of inertia guys so this Sumas into this radius of variations of square foreign [Music] are attached as shown or in the figure okay it's okay as shown from the system wording ticket radius okay the moment of inertia of this system about an axis perpendicular to plane okay plain La perpendicular and passing through Center of this is about Mr Square by 2s plus yard is some moment of inertia about this particular axis is actually m r Square by 2 on this particular axis is equal to plus MH Square Parallax serum plus m h is 2R MH Square addition m r Square by 2 plus again m r Square by two plus uh 4 m r Square number B question number 18. particle is moving uh in uniform circular motion with speed V and radius r angular acceleration of particle is is angular velocity V by our restaurant is a velocity is a value divided the angular velocity changes never for angular acceleration is angular acceleration here clearly zero is not an option number D okay question number 20. 20 uh yeah lessons actually okay misplaced 21 see particle is performing uniform circular motion along a circle of radius r t k R radius the circle in half the period of revolution when say half Revolution displacement distance and distance covered is circumference that is fire foreign correct so displacement is two R and uh distance covered is fire 22 question number 22 bar body is rotating about its own axis its rotational kinetic energy is X okay half I Omega square is X and its angular momentum is y angular momentum I Omega is actually y which are that kind moment of inertia about axis is a 1 divided by two two I one though one by two I is equal to X by y Square so 2i is a value y Square divided so two degrees so moment of inertia is a value y Square divided by 2X y Square divided by what 2 x okay next sum question number 20 uh three disc has a mass m and radius r I like disk using mass m is okay so how much tangential Force should be applied to the dream yeah so as to rotate uh with angular velocity Omega in time t foreign system on the distance tangential Force into the axis passenger distance the force whatever calculation R cancel a square cancel Force m r Omega by 2T m r Omega by 2 T option number B PL Force okay question number 24 questions bucket containing water is revolved in a vertical Circle the vertical Circle to prevent the water from falling down what the velocity by imagine the velocity velocity should be under root of GR but which are the minimum frequency of revolution so Omega should be equal to under root of uh foreign uh two bodies of mass m and three m okay are rotating in a horizontal circle of radius R and 1 by 3. 1 by 3 R sorry R by three tangential tangential speed of uh body of mass m ithesis is the radius it's a radius R by three liter uh tangential speed of mass m is n times that of mass that of heavier Mass so this is the velocity and N times heavier muscle and behavior mass of velocity V Masa velocity is NV Logan's a centripetal force centripetal force cast to m V Square by R so as a centripetal force m of V Square by R is R by 3. foreign okay that half MV Square Mass constant speed constant so kinetic energy one constant but momentum constant momentum is MV velocity is the direction changes acceleration acceleration is a value constant type but acceleration the direction is always true to the center so hurricane pointer acceleration the direction has changed fire question number 27 solid sphere of radius R has mass m moment of inertia of a solid sphere about an axis at a distance R by 2 from the center okay again solid space amount of inertia about diameter a two by five Mr Square Alabaster correct at the axis Parallax is two by five m r Square correct plus the access about moment of energy is 2 by 5 m r square plus m h Square h hapla r by 2A bro so Chi mineral calculation two by five m r Square Plus um Mr Square by 4 1 Omega Valley cross multiplication 4 into 2 is 8 m r Square plus this is 5 m r Square divided by because approach that is equal to 20 so 13 Mr Square divided by 20. our plants are one so 13 m r Square divided by 20. okay next question uh question number 28. question number 28. okay so uh a solid sphere of mass m and radius R is rotating about its diameter solid sphere okay so moment is a two by five Mr Square okay a solid cylinder of same mass and same radius is also rotating about its geometrical axis radius same moment of inertia has to solid squares cylinder cylinders are accessed about m r Square divided by 2 hours cylinder acts as a disk just the thickness same mass same radius is also rotating about this geometrical axis with the angular speed twice that of sphere spheres angular speed Omega also the result 2 Omega the ratio of kinetic energy of spear to cylinder kinetic energy of sphere divided by kinetic energy of cylinder okay that is equal to kinetic energy is a Formula I have I Omega Square divided by half I Omega Square half of cancel at the moment of inertia sphere Chi two by five m r Square m r Square by two foreign cancel correct versus either four by five so four divided by 5. Omega Square Omega Square cancel 4 4 1 cancel or not so one one by five answer one is to five correct so 29. question number 29 uh when a blob of mass m moves in horizontal circle of radius r with a universal V having the length of string l conical pendulum length of string is l okay half here to a goal radius radius uh I guess semi vertical angle is the centrifugal force acting on The Bob will be centripetal force T sine Theta correct ly and T sine Theta basically yeah t sine Theta acts as a centripetal force okay cos Theta is equal to mg so tensions that is T sine Theta okay that provides centripetal force actually T sine Theta when tensions into sine Theta so sine Theta by cos Theta let me directly tan Theta value plus centripetal force what is time Theta time Theta means opposite side Theta is opposite side that is r divided by adjacent side height height R square foreign okay question number 30 a ring solid sphere and disk have the same mass and radius second is a mass and radius same which of them have the largest moment of inertia ring ring someone to finish is Mr Square solid sphere so amount of energy is two by five Mr Square okay and the disc this amount of energy is or Mr Square by 2. so again the radiation definitely uh Rings amount of inertia foreign number eight question number uh 31. in non-uniform circular motion ratio of tangential to radial acceleration about tangential to radial acceleration tangential acceleration angular acceleration into radius acceleration V Square divided by what r r versus V Square option number D okay a can filled with water okay is reward in a vertical Circle vertical Circle circular motion uh radius time period of revolution foreign foreign okay next question question number uh 33. okay kaipa satellite of mass m okay let us say for instance this Earth and like satellite is capital M so satellite around the earth or around the planet orbit of radius orbits the radius which are the angular momentum of satellite about Center of orbit will be what angular moment in terms of formula MV are satellites objects angular momentum has a mass into this velocity into this Omega Square and there's an angle a moment of inertia as funny velocity angular velocity V by rs2 RR cancels so MVR as a angular momentum mass of satellite at the velocity is Lego velocity satellite velocity critical velocity velocity gravitational the velocity under root GM where m is the mass of Earth velocity divided by r so Yoda centripetal force locked though that centripetal force is provided by okay gravitational force attraction Force GMM by R square cancel velocity is a Formula under root GMO foreign cancel okay so M into under root of g m r as answer but happens option number D is question number 34. a relative angular speed of r hand and the second hand relative speed is 40 meter per second foreign foreign okay relative angular speed of our hand and the second hand our hands angular angular velocity shows angular velocity is the formula so two pi divided by time period our hands a time period okay so time period is 24 12 hours and one hour means uh 60 minutes and one minute means again 60 Seconds angular velocity our answer second hand is angular velocity part 2 pi divided by um 2 pi divided by secondhand's uh uh angular velocity is 2 pi divided by time period second hand is a time period 60 seconds only foreign correct relative angular speed is so 2 pi by 60 minus of 2 pi divided by or 12 into 16 to 60. if you make it worth it so that denominator is three six zero zero product into pi T minus of 2 pi divided by is I think one four three eight pi seven 1 9 as a litera at least seven seven one nine pi put on on a seven one nine pi divided by the other one's a product is two one six zero zero two one six zero zero option number c m next sum question number 35 okay uh okay horizontal circular motion with a constant angular velocity and its angular momentum is l have a angular momentum M into V into R but R height length so angular momentum if the string is now halved stringless keeping angular velocity same angular velocity then the angular momentum will become what bhagata objectives M into radius of square bro into angular momentum sorry angular velocity angular velocity as it is foreign foreign so he has a moment of inertia M into this R square M R square a moment of inertia into Omega Omega now the strings so automatically angular momentum so L by four T next sum question number 36 a van is moving with a speed of one zero eight kilometer per hour one zero eight kilometer means Hazard meter one arm is three six zero zero seconds correct so head on zero head on zero cancel correct 36 are table thirty six three thirty six one worthy Thirty One Thirty meter per second speed so velocity is 30 meter per second level road travel coefficient of friction has 0.58 okay and radius of curvature shall be for a safe driving of van the minimum radius of curvature should be cash the pressure safe speed is horizontal turnover either velocity is under root of coefficient of friction is 0.5 1 by 2 literally the radius well and that is equal to 5r so R is a value of 180 option number c t next question question number 37. moment of inertia of ring about axis perpendicular to its plane and passing through Center ing some moment of inertia M R square is then moment of inertia about the tangent in the plane ever ranges moment of inertia about diameter m r Square by two also about tangent in its plane study plus Mr Square H about Mr Square by 2 plus m h square m h Square so have one to three by two m r Square tangent about moment of inertia 3 by 2 m r squared but m r squares should be six is [Music] uh a weightless string can support the tension of 30 Newton okay X string is okay 30 Newton's attention support stone I have 0.5 kgs of radius 2 meter in a vertical plane vertical circular motion then the maximum angular velocity of stone will be what if a string breaker chances foreign MGI so tension are 30 minus of mg words of force minus Khalsa Force okay centripetal force maximum angular velocity um okay so 25 should be equal to mass again 0.5 radius he 2 meters radius Omega okay into Omega Square have one Manila so Omega Square 25 Omega should be equal to 5. 5 radian per second a maximum angular velocity question number 39. relative angular speed of our hand and minute hand yeah another last question a particle moves along a circular path of radius r with a uniform speed V then angle described by particle in one second is actually so angle described by particle in one second when this angular velocity of each other an angular velocity might be available option number D okay rotational Dynamics equations uh CTC okay the session if it is

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Id: Biad-ouDAAQ

Length: 70min 10sec (4210 seconds)

Published: Wed Nov 23 2022