and people hope this session is going to be a rocking session um foreign stay tuned okay so hope you all get a perfect idea of what we are going to do now completely exactly in the head foreign foreign Kardashian foreign magnitude foreign foreign directions scalar quantity foreign foreign so let's start foreign foreign upper we are mentioning with respect to origin suppose either y-axis governing for example okay for example for example angle directions so mentioning a vector mentioning a position position Vector with respect to Theta okay okay foreign either way so that means foreign minus very simple very simple either a vector either B Vector path correct exact other meaning no problem another zero degrees so that means Theta will be 180 degree okay okay magnitude foreign a perm aintenance foreign [Music] foreign we are having a plane place that is so let us say is foreign so that is your co-planar Vector first condition another magnitudes okay but but listening 90 degrees angle okay but Theta should not be 90 degree okay but Theta should not be 90 degrees okay fine now next step concurrent Vector okay in the concurrent Vector simple you are having a point okay vectors so all vectors passing through a single point huh single point denotes Direction I've been getting enough for example okay for example listen foreign Victor a Victor divided by modulus so this is a main important thing now here comes okay it is all parallel vectors are equal vectors all parallel vectors are equal vectors equal vectors so that means this is false it is false correct either false so next I hope white will be better correct so I hope white will be better false all equal vectors are parallel vectors so this is true now the next one all anti-parallel vectors are opposite vectors all antiparallel vectors or opposite vectors anti-parallel vectors but this is false opposite vectors always anti-parallel ISM so this is true now the next setup anti-parallel vectors may be opposite vectors antiparel vectors may be yeah maybe maybe you know so maybe right all collinear vectors or parallel vectors collinear vectors no so it is false may be anti-parallel vectors always equal vectors because linear vectors are always equal vectors equal vectors but collinear vectors right so that means it is false foreign all concurrent vectors or co-planar vectors all concurrent vectors or coplanar vectors exactly that is true so that means this is true all coplanar vectors are concurrent vectors all coplanar vectors or concurrent vectors this is so this is false okay so the final condition in all concurrent vectors may be collinear Vector something right um vectors okay yeah all concurrent vectors may be coplanar maybe maybe so this is also true this is also true okay so pasanglam is Newton's Laws of Motion is okay yes so now the next topic okay types okay yes so let's start okay let's start um so let me say more than yes so next yep so next parting of D now triangular law of additional details arrangements so listen Maybe separate vectors a vector okay either one the B Vector okay okay so first thing is triangular law of addition the Triangular log main rule this is your secret true secret rules the emergency rule this is the Only Rule that is head to tail connection head to tail connection head to tail connection um original foreign foreign foreign foreign Theta results foreign foreign so that means foreign foreign so let's go for the next one foreign the DNA resultant will be equal to square root of a square plus d square plus 2 a b cos Theta materials variations we are saying that as Alpha normal formula normal formula the normal formula is very clear for you right now variations resultant will be equal to root of a square plus b square plus 2 a b cos Theta foreign a square plus b square plus 2 A B A plus b the whole Square format upper root of root of a plus b the whole Square format up in the square root cancel resultant will be equal to root of resultant will be equal to paper Next Step is will be equal to B sine Theta divided by a plus b cos Theta correct sine zero degrees divided by a plus b cos 0 degree sine zero degrees tan Alpha will be equal to will be equal to root of a square plus b square plus 2 a b cos 180 degree 180 degree will be minus one up a square plus b square minus 2 a b negative equal a minus r will be equal to a vector minus foreign equal to triangular opposite opposite vectors okay now next that is B sine Theta sine Theta divided by a plus b sine Theta correct up a plus b sine Theta is Theta Verma foreign correct so that means resultant will be equal to root of a square plus b square plus 2 a b cos Theta in that 90 degrees is so that is tan Alpha will be equal to B sine Theta divided by a plus b cos Theta negative B sine 90 degree divided by a plus b cos 90 degree negative so cos 90 degree 0 by rho B sine 90 degree sine 90 degrees another one that is the maximum value right that is the maximum value upper B divided by a updated B divided by a of directly tan Alpha so now the next important thing okay so the next important and most important thing if a vector is equal to B vectors root of foreign foreign that is that is 1 plus cos Theta will be equal to 2 sine Square Theta sorry 2 cos Square Theta by 2. 2 cos Square Theta by 2 Now 1 minus cos 2 sine Square Theta by 2. so this will become 4 a square cos Square Theta by 2. in the 2 when the 4A cancels okay foreign foreign a plus b is yes so let's see let's hope so resultant another number please a square plus b square plus 2 a b cos 60 degree right cos 60 degree now another cos 60 degree of D now one by two right up a square plus b square plus 2 a b into 1 by 2. a square plus b square plus 2 a b divided by 2 2 cancel it this will be a square plus b square plus a b simple right either way if they are asking you a direction upper Direction formula another tan Alpha correct Alpha so that will be B sine Theta divided by a plus b cos Theta correct B sine Theta sine 60 updating another root 3 by 2 correct term that will be root 3 by 2 divided by a plus b 1 by 2 right so root 3 B divided by 3 B 2 2 A plus b the whole Square two two cancel IDs root 3 B divided by 2 A plus b okay that's it okay either way 120 degrees minus one by two R com sixty degrees this is your complete analysis okay okay yes foreign we used to say it is 180 minus Theta updates right upper in the type of questions occurring a triangular logic series it is how we can identify our so see RFD identifies R Vector will be equal to root of okay R Vector will be equal to root of a square plus b square plus 2 a b cos Theta is the angle between both vectors upper that is cos 180 minus Theta and cos 180 minus Theta anger than is a minus cos Theta is trigonometric identities suppose in the COS Theta is is foreign procedures will be root of if Theta is equal to zero of Dena root of a square plus b square minus 2 a b abdom correct already so either when the minus cos Theta so minus a minus right either way either way clear our come play so now the next one of 180 degrees R will be equal to root of a square plus b square minus 2 a b cos Theta is 180 degrees so that will be a vector minus plus b Vector in the conditions is 90 degree 90 degree now it's very simple right 90 degree now 90 degrees root of a square plus b square minus 2 a b plus b square minus 2 a b cos Theta 90 degree when the chapter zeros and the whole term upper a square plus b square the whole root tan tan Alpha is B sine 90 degree divided by a minus B cos 90 degree either 0 by Dome either one the one item so that will be B divided by a tan Alpha negative okay so B divided by a tan Alpha negative foreign B Vector okay one either R resultant a plus b Vector is smaller Arc other acute angle so Theta lesser than 90 degrees let us draw a parallelogram even a parallelogram s is greater than 90 degrees foreign foreign okay yes so now dot product cross product the vector multiplication so in the vector multiplication because let's do with lot of energy okay so dot product cross product okay so let's talk about each and everything dot product cross product okay so listening on the render vectors for example listen foreign formula it is a vector dot b Vector will be equal to modulus of a vector into modulus of B Vector into cos Theta in Earth zero degrees so cos Theta will be equal to a dot b divided by a vector into B Vector okay foreign will be equal to minus modulus of a vector my modulus of B Vector negative minus one right now the next 90 degrees because cos 90 will be equal to zero a vector a vector dot b Vector will be equal to 0 update okay by a vector will be equal to zero yeah okay now properties up in the dot products dot product is okay now the next one application is for example work is equal to force into distance Force dot distance okay that is very very important over here 90 degrees okay so these are very important dot product or unit vectors because dot products results x axis Y axis Z axis minus x minus x minus I cap is now so listen dot products 90 degrees will be equal to 1. either way I cap dot j cap is equal to J cap dot k cap will be equal to K cap Dot I cap will be equal to zero okay okay foreign conditions foreign right hand rule right hand rule right hand screw rule is foreign C has a direction of outwards foreign foreign foreign that's very simple cross product or rule Theta zero now sine zero will be zero upper a cross a vector dot cross B Vector will be equal to zero simple will be equal to zero 90 degrees cross B Vector will be equal to modulus of a vector modulus of B Vector PSI 90 degrees the answer foreign I cross I will be equal to J cross J will be equal to K cross K will be equal to 0. right either one is will be equal to J cross k J cross K will be equal to sorry K cross I okay K cross I will be equal to 1 will be equal to one either conditions so the next thing foreign foreign foreign anti-clockwise automatica what will be the anti-clockwise method so anti-clockwise method abdina I cross J is prefer red so I cross J J cross k k cross I okay okay I cross i j cross J K cross K is equal to 0. clockwise okay identified modulus now diagonals of diagonal one into diagonal two cross okay one and foreign will be equal to radius this is your condition just give me a minute okay so now what are the things we have already discussed so types of vectors okay Vector resolution okay so the vector resolution is y-axis so that will be listen horizontal components component vertical components vertical component of the inner Rend component real life foreign foreign come on x axis Y axis either when the numerals cos Theta okay sine Theta adjacent in the vector when the suppose foreign adjacent side horizontal components Theta foreign foreign foreign it's very simple listen actually the three dimensional x axis y axis foreign foreign next in the z-axis I hope it is so what is the formula for cos Theta cos Theta will be equal to adjacent Side by hypotenuse character hypotenuse is the number formula adjacent side hypotenuse hypotenuse resultant will be always called as hypotenuse gamma foreign foreign beta foreign foreign Cartesian foreign simple result foreign ratio will be helping to find direction cosine if foreign foreign right this is the main thing is so listen either so what will be the answer L square plus M square plus n Square will be equal to 1. foreign hmm okay the sine squares sine Square what it is is square beta plus sine Square Alpha is sine Square Theta can be written as 1 minus cos Square Theta correct identity is plus 1 minus cos Square beta Plus 1 minus cos Square Alpha is three plus okay 3 minus cos Square Alpha plus cos Square gamma Plus okay beta plus cos Square Alpha so you have to keep this in mind either okay it is important so let's go for the next one now projection or components of vector projection so for example wait let me foreign 50. wait let me write it in a different color so B Vector a project is foreign modulus of B Vector cos Theta foreign foreign foreign foreign listen carefully foreign squared Ness cross product foreign first I cap okay plus minus plus the alternate plus alternate plus and minus foreign foreign Next Step next category is foreign foreign Plus a y plus b y into J plus a okay plus a is that plus b is it into K minus minus are very simple okay so minus 119 minus so a x minus b x into I cap plus a y minus b y j cap Plus foreign ethereum reference just to go and watch your previous video One Dimensions okay foreign foreign write either origin 0 comma 0. we have to understand is foreign foreign simple okay now displacement Vector is shortest distance final Point minus initial Point correct term up a short test distance but final position minus initial position either the final position upper displacement can be written as a b vector foreign foreign let us see foreign so V Vector will be equal to suppose two dimension of Dina velocity at x axis into I cap plus velocity on Y axis into j k either way acceleration acceleration will be equal to net acceleration boom foreign wait so now the next criteria white color upper vectors addition subtraction multiplication dot cross resolution analytics plane in motion of the coupler the acceleration in a acceleration another Motion in a plane acceleration exactly 60 of your syllabus got over Evolution 60 of your syllabus got over in addition you know forty percent projectile motion relative motion uniform circular motion now projectile motion projectile motion number one dimensions of okay foreign foreign because so listen yeah okay is for example listen um so for example is on two types of projectiles in the two types of projectiles were protected with numericals derivations let us make this page okay let us make it dark foreign acceleration due to gravity is foreign so listen when a particle is thrown with some velocity and after that it's solely move under the influence of gravity so listen or a particular distance [Music] that is a parabola okay but be patients so let's go for that yes foreign time of flight time of us foreign next criteria fight okay what height okay is the height sorry height so height is maximum height at any point fight at any time okay okay when time will be equal to Total flight time divided by listen okay one so first main thing um [Music] foreign [Music] [Music] V sine Theta is parallel to Y axis V cos Theta is parallel to x-axis now the next thing is covering a horizontal distance correct in the horizontal distance which is very very beautiful thing maximum height in the range complete range and a half the maximum height in a total of five centimeters foreign formula this is your formula okay it is so now listen this is a very important thing is the constant V cos Theta bringer throughout the projectiles because that means only V sine Theta will be varying yes at an angle okay so now the next important part okay so the initial velocity is ascent time so final velocity will be zero upper 0 is equal to initial velocity is G okay um initial velocity will be zero final velocity will be V sine Theta or U sine Theta yeah up okay and time of flight time of flight is nothing but so time of flight will be equal to time Ascent plus time this sentence U sine Theta divided by G plus u sine Theta divided by G so that will be time of flight complete flight will be equal to 2 U sine Theta divided by G of D negative okay okay so let's start the next one maximum height another height total equation types of formulas total time divided by 2 hours that will be we are going to solve using second equation which is V square is equal to U square plus 2 yes so what will be your initial velocity initial velocity will be 0 is equal to U Square sine Square Theta is [Music] U Square sine Square Theta divided by 2 G is equal to H maximum so this is your H formula H maximum use 90 degrees but no problem this is the main important thing it's very simple s is equal to u t plus half a t Square okay okay so height will be equal to U sine Theta okay T another U side U sine Theta U sine Theta divided by G updated plus okay minus minus half J K Times Square upper U Square sine Square Theta divided by G Square updated U Square sine Square Theta by G minus half U Square sine Square by G total value minus number one minus 1 by 2 1 by 2. very simple very very simple okay yes that is a logic okay so now the next one is trajectory okay wow so trajectory is a very important thing in order five to six minutes because it is very important okay so trajectory of Dina in the complete in the path trajectory of Dean trajectory and the trajectory of the earth Express foreign writing so that means U cos Theta into T character into T will be equal to X so this is rx y will be equal to u t plus half a t Square updates foreign foreign foreign X tan Theta minus half g into x square divided by U Square cos Square Theta okay upper this is one of your formula okay either project trigger one of the formula is so this is one of your formula is listen carefully foreign Y is equal to X tan Theta minus half J into x square sine Theta divided by U Square in the COS Square cos square and I will be cos Theta into cos Theta into sine Theta update so next Next Step is y is equal to X tan Theta minus half j x square tan Theta divided by U Square cos Theta sine Theta DNA either one of your trajectory formula is Y is equal to X tan Theta minus half energy here I am just dividing others so dividing by G in there is x square tan Theta divided by U Square cos Theta sine Theta divided by G Narco okay and the range of equations it is your range formula this is your range formula range formula is okay one this is another one expression foreign tan Theta that is tan Theta by 2 by R okay tan Theta by R numerals okay so hope you understood everything now in the next part foreign what is the range foreign sine Theta 2 U sine Theta divided by G in academy either I can write U Square 2 cos Theta sine Theta 1 whole divided by G negative so either one of your range formula either one of the range formula okay one is if Theta is equal to 45 degree then sine 2 into 45 updated which will be equal to sine 90 degrees which will be equal to sine 90 degree sine 90 degrees that will be one so finally upper maximum range so maximum nothing but if beta is equal to 45 then range will be equal to R match a power Max or the formula R Max or the formula will be U Square sine 90 divided by G this whole value will be 1. U Square divided [Music] this condition maximum range is 45 degrees a square divided by 4 a square divided by 4B of being meaning okay so these are your range angles complementary angles for example nine ninety minus 30 degrees so that means sine 16 okay sorry sine 40 degree will be equal to cos 60 degree a percent 30 degree another one by two others complementary angles so R will be same either one is yeah R will be same for complementary angles okay R will be same for complementary angles this is very important okay now the next step other way complements even when the suppose 30 degrees so that is your range okay so complementary angles 35 degree of dinner that will be 30 degrees so simple just go through this now the next important thing is velocity at any point is foreign wrote off v x square plus v y Square v x sub D9 what is v x square VX U Square cos Square Theta vigorical v y Square update U Square sine Square Theta minus G Square t Square okay next step suppose tan Alpha tan Alpha is divided by VX that is U sine Theta minus GT divided by U cos Theta is foreign again the next important term we are going to study is angle of elevation angle of elevation is distance foreign this is your y formula okay because because displacement displacement r at any point okay one upper angle of elevation of DNA is a very important Concepts don't forget foreign [Music] you can find the magic okay yes so the next point is momentum change in the momentum change is literally important be careful so momentum change so listen foreign so DP can be written as minus m g t j cap acceleration foreign foreign okay so this is very clear right now yes now it is [Music] for which both the horizontal range and the maximum height are equal to maximum horizontal range so let's start solving in the given data okay okay sine Square Theta divided by 2G is equal to U Square U Square range or is that is r 4. foreign listen foreign foreign so next will be H is equal to U Square divided by 4 gen in radical and if listen carefully or important thing okay horizontal 45 degrees our maximum will be equal to 4 h so four times of the Horizon four times of the vertical height option D is your correct answer okay I hope everything is very Crystal Clear again next to Newton's Laws of Motion on the conference okay now the next question a cricketer hits a ball with a velocity of 25 meter per second at 60 degree above the horizontal or a cricketer okay initial velocity is how far above the ground it passes over a Fielder 50 meter from the bat although the field let us visualize foreign foreign okay one minus X tan Theta g x square hold by 1 by 2 U Square cos square square cos equations so 25 into 25 into cos Square Theta upper cos Square 60 25 into 25 5 to 12 plus 0 1 4 so 5 25 so it will be 525 1 4 5 6 25 answer okay what we will be getting 625 so 625 into cos 60 update another one by two so upper 1 by 2 whole Square Now 1 by 4 negative ones are twos 50 root 3 minus nine point eight into two thousand five hundred into two whole divided by 625 you will be getting y value 8.2 meters eight point two meters it's completely up to you okay so let's start let's go for the next one next question okay so next question is the equation of projectile is y is equal to root 3 x minus g x square g x square by 2. Y is equal to root 3 x minus j x square by two the speed of the projectile is okay because Y is equal to root 3 x minus half into j x square if the number formula x minus half g x square divided by U Square cos Square Theta Theta should be 60 degree because tan 60 degrees foreign okay so now the next one so the next thing what we are going to focus is this will be considered as the height sine Theta foreign [Music] root of v x square plus v y Square Theta suppose foreign X angular so this is v x divided by V in it correct up v x divided by V in it okay so hope everything is [Music] so let's start with projector horizontally with a speed of 20 divided by root 3 meter per second okay 20 divided by three so this is your projectile we can write acceleration is equal to V by danger G is equal to v y divided by T in the time can be written as v y divided by G is so how we can find out v y v y y axis B initial will be 20 divided by root 3 into I cap updates right so that means so we can write so final velocity will be equal to V into cos 60 degree I cap plus v into sine 60 degrees that will be 1 by 2 cross multiply 40 divided by root 3 is equal to we identified foreign that will be 2 second so the perfect answer will be option D okay okay so fine we have identified this yes we are going to discuss some basics so listen River Crossing relative motionless it's very very important to listen first foreign velocity is correct um correct very simple listen if foreign this is very important okay okay stand still stand still Upstream under the downstream okay one stand still okay opposite opposite 180 degrees velocity of man with respect to River foreign foreign foreign okay yes fine if the next step are the important is v b sine Theta to cross foreign so time for drifting time for drifting correct terms plus VR into T is equal to X is Theta into t plus v r into T is equal to X in the VB cos Theta into T velocity because of okay the velocity because of both is done okay it will be fine okay one now the next thing drifting line in terms but it's very simple okay hope the next one you will learn a special case special cases minimum time velocity [Music] foreign foreign foreign trigonometry will be helping to the Core foreign foreign baby foreign which will be VR divided by root of VB Square minus V R square foreign so now let's do some numericals okay one let's do some numericals about the scent across a river with a velocity of eight kilometer per hour then the velocity of the reverse foreign what will be the VR so v r will be root 36 which is 6 meter per kilometer per hour because so the perfect answer is option b clear outcome so it will be very very easy Concepts now the next question a person aiming to reach exactly the opposite exactly the opposite path concept shortest path on the bank of a stream yes swimming with a speed of 0.5 velocity even the 0.5 meter per second at an angle of 130 degree at an angle of 130 degree with the direction of flow of water the speed of the water in the Stream is 90 degrees upon 90 minus I mean 220 will be 30 degrees 30 degree foreign it's very simple so hope you are enjoying the like buttons so don't forget to press your like button okay let's start that's it emotional let's draw a circle first foreign velocity acceleration displacement is okay yes huh cool so listen is foreign vector foreign centripetal force centripetal force of Dino Force centrifugal forces it is a radial vector radial Vector in the radius centripetal force always act towards the center apply the centripetal forcing in the radial Vector centripetal force acceleration radial acceleration radial acceleration radial acceleration tangential Vector um so for example if the radius so this is our radius parameters velocity so velocity of the circle will be tangential vector tangential vector okay it is your acceleration will be equal to radial Vector is a tangential Vector okay one and is so now the next important thing circular motion topic foreign uniform circular motion normal uniform motion what is uniform motion uniform motion of DNA velocity acceleration or restylar objective so uniform circular motion foreign this is your tangential acceleration so acceleration and the acceleration two types of accelerations acceleration two types of accelerations will be given so this is the concept you understood clearly foreign circular motion circular motion is okay one acceleration is we people know listen carefully we people know uh either uniform motion vector magnitude is okay so I hope everything is clear now if the directions V final minus V initial 90 degree what will be the formula resultant Vector will be equal to root of va Universal root of v a square plus v b square plus 2 v a v b cos Theta correct zero item so that will be root of v a square plus v b square 3 square plus 3 Square will be 9 plus 9 root 18. that will be 3 root 2 meter per second foreign but it can't be zero it can't be 0. we have to exactly the zero degree 180 degrees that means listen carefully access it is foreign how we are writing it as so listen that will be 3 into minus I cap so that will be plus 6 I cap I capitalized whenever you're having facing 180 degree or zero degree just go for directions hope it is very very clear for you now the next question is foreign cos Square Theta by 2 other way 1 minus cos Theta operating greater than the sine Square Theta by 2. so you will be getting minus because the main reason is VBA final v e B minus root of v a square plus v b square minus 2 v a v b cos Theta correct I then result into minus cos Theta 9. okay hope it is very very clear now angular displacement okay so is let us discuss what are the angular displacement so either when the radius foreign we have to use right hand screw rule right hand screw rule either positive okay that will be Theta into Pi by 180 either way Radiance every month radian into foreign things you have to understand so next angular velocity angular velocity so normal velocity in another Distance by time taken applying the angular velocity that is suppose average which is Theta 2 minus Theta 1 divided by T2 minus T1 either way instantaneous frequency of Green Solution angular frequency is frequency is nothing but okay wow number of rotation or number of rotation or number of Cycles are number of revolutions okay our number of Beats per second our number of oscillation or number of oscillations per second it is main thing is which is equal to axillary tangential acceleration so Alpha will be equal to Omega by T abdinary radian per second Square okay next step average acceleration of D now Omega 2 minus Omega 1 divided by T 2 minus T1 are they radian per second Square either way instantaneous [Music] second wire okay so these are the important things you have to analyze if the Next Room three rotation okay one three rotation Inner Circle updates will be equal to number of rotations what we have to identify so number of rotation will be equal to Theta divided by 2 pi update number n is equal to Theta divided by 2 pi updated Q okay so for example if the 360. so 6 Pi Pi update 180 upper 180 into 6 and then 0 48 46 into 180 degree zero eight four six n will be equal to this is your formula number of rotation okay one number of rotational either one of the formulas again hope you are understanding everything conversion frequency rotation per minute under X into okay so X into 2 pi divided by 16 to 60 either way seconds 2 pi divided by 12 into 6 into 660 into 60. okay so the main conversion now kinematic equations so linear motion second formula s is equal to u t plus half a t Square b square is equal to U square plus 2 a s okay one now okay with alarm Omega 1 plus acceleration again the alpha into t Omega 2 square is equal to Omega 1 square plus 2 into Alpha into Theta upper it is okay yes now radial or centripetal acceleration okay one so radial acceleration and then starting a solution that is centripetal acceleration is which will be centripetal force correct term so f is equal to M into AC okay M into AC F in the radial acceleration radio acceleration give a about this so that is the main thing V Square divided by r linear velocity linear velocity okay the radius of the circle okay radius of the circle upper centripetal acceleration that is towards the center so number radial acceleration something which is radial radial meaning period that is towards the center acceleration will be directly proportional to radius into acceleration will be directly proportional to radius into alpha alpha 9 is the other tangential acceleration in the acceleration in the acceleration linear acceleration up a linear acceleration we don't say centripetal acceleration in the linear acceleration Zone separate universe if you are having a circle or a circle radius okay one so tangential velocity acceleration is listen foreign C clear outcome so this is your tangential acceleration Now directions of tangential acceleration now let's start for example either when the acceleration okay okay so now the next important thing is tangential velocity in a velocity it is acceleration net will be equal to root of a t square plus a c Square update is foreign this is your okay I hope it is very very crystal clear now linear versus angular okay listen carefully first velocity velocity is velocity will be equal to R into Omega velocity will be equal to R into Omega so that means the angular velocity Next Step displacement okay one displacement best placement is equal to R into Theta Theta is a tangential acceleration so tangential acceleration here a is equal to V Square divided by R of denominated either when the centripetal is the tangential in a tangential than a linear suppose centripetal of DNA B squared r Square Omega Square divided by r r cancels centripetal acceleration so these are the concepts you have to keep in mind okay yes foreign the angle made by its acceleration with its velocity is others accelerations acceleration accelerations so they are asking acceleration acceleration velocity okay so this is foreign first we people know which is so we are asking this value acceleration if they could angle made by its acceleration with its velocity okay so listen either 90 degrees okay it's very very easy question so listen carefully first let us solve you know AC will be equal to what is the value V Square divided by R which is 20 into 20 divided by 80 updating so 0 0 1 4 1 5 so that is 5 meter per second Square foreign so Theta value will be Theta when the 45 degrees so Theta will be 45 up in the Theta value another number 45 correct time so acceleration velocity in the angles which is 180 degrees so the value will be 180 minus Theta which is equal to so 180 minus 45 will be 135 degree correct term 135 degrees yes 35 degree so the perfect answer will be 135 degrees so that is a total angle okay so that is the total angle now the next question are the questions the angular velocity of a wheel is 70 radian per second okay so angular velocity of Omega is equal to 70 radian per second rotation 70 into 2 pi divided by 60 into 16 reported either radian per second substitute yes if the radius R is equal to 0.5 meter then the linear velocity of the wheel is linear velocity will be equal to R into Omega yes linear velocity very very simple okay yes so Dina [Music] so what we are going to do only thing study work hard whatever it takes okay and most probably Victor and Mara bats online you can collect your informations okay so that's it for today because physics okay bye everyone take care have a great day foreign