JEE Mains and Advance Physics || Constraint Motion || DSA

[00:00:11]hello motivational [Music] is constrained motion [Music] movement the movement of one body or one object will affect the movement of other bodies [Music] the motion of one body will affect the motion of other bodies the connector body motion of connected bodies actor string they are connected the acceleration same protector constrained motion product constrained motion money m1 edge acceleration m2 accelerations hello why imposed on motion motion is a restriction relation position or both of system of particles is known as constraints constraint limit the motion of an object suppose your movement is dependent on the motion of other motion of other constrained motion method motion restricted assay by the movement of other set eyeballs the restriction imposed on a motion or position motion report but positional but both which cannot proceed arbitrarily never possible motion results when an object is forced to move in a restricted way act object k on force restricted single pendulum is a constrained motion as it always remains at a fixed distance from a point of suspension train [Music] moving on the surface of a sphere is restricted as it can move either on the surface or outside the surface surface abacus is constrained in one dimensional by supporting the virus system motion of a gas molecule in a spherical container container a gas molecule is a motion blur regulator constrained motion gas molecules on hydrogen hh hydrogen then only h is restricted by the other one it's a constrained motion the motion of a rigid body as distance between any two particles remains constant rigid examples [Music] so so okay okay if we consider two bodies of body i'm gonna consider kodi connected with each other there are actual foreign connected and moving together they move courses that their velocities are accelerational velocities and accelerations are related relation between those quantities a velocity velocity relation acceleration acceleration relation is a relation capable of constrained relations here in this lecture lecture is um foreign instant thick oe moment j moment a angle 37 degree it has string length length second m velocity find velocity of m m velocity valley most helpful hobby most helpful of a tower drawback start by subscribing and secondly process one top eight ipad system and capture they can actually kind of hypotenuse foreign we will solve using three processes power power power we will solve this sum by three processes method one pythagoras theorem pythagoras theorem like this like this we're gonna act a triangle consider kurthupari like this let this be z it takes a y foreign consider column this one is x this one is y this one is j but i can click the verbo square plus y square equals to z square tio's good x square plus y square equals to z square title angle to 37 degrees angle 37th i'm going to get into wire values five differentiate differentiating with respect to time differentiate curve time and respect x square differentiate correlate two x d x d t y k differentiation b [Applause] is you can take a perpendicular draw correct position a to cool length so z will change that means x will change but y will remain constant judging by differentiation zero differentiation two two cancel away x into d x d t is equals to z into d z d t m1 at velocity v2 and velocity suppose v1 when a direction active velocity cut scores either character velocity cut scorcher v1 indicator velocity that since dx dt is equals to dx dt is equals to v2 and dz dt is equals to v1 foreign x direction a rate of change x direction a rate of change instantaneous velocity concept instantaneous velocity instantaneous velocity instantaneous velocity issue of v equals to dsdt v equal to dsdt limit the instantaneous velocity s with respect to time change of s with respect to time kinematics one motion in one d kinematics one d instantaneous velocity x a data change that is the velocity of the particle xa move quartz m2 is moving along x-axis the exit data change x is the displacement exceed data change shutter improve velocity rate of change rate of change color dx dt v2 dxdt v2 [Music] v2 velocity now the interesting fact z v1 kikorevolo dz dt rate of change of z v1 rate of change of z dz dt is yv1 that is the velocity of m1 cano exactly the one centimeter one centimeter if this body moves one centimeter rope length of rope will always remain constant length of rope will not change [Music] [Music] square plus y square is equals to z square differentiating with respect to time x to the power n a differentiation n by rho s way x 2 of x square x is square root of 2 x m neh n by rho c x to the power 2 minus 1 2 x j to timer respect to k d very foreign one so fast fast uh foreign um cookies no doubt sure one two three go get a repeat telecast power relation or power method power kamuta velocity good force our velocity we know we know power our velocity dot product by that is internal force concept of internal force see [Laughter] internal internal forces can't move the body [Music] 0 internal force zero into air force scale force cancel coach air force care force cancel coach area net zero bullet into system and move watching a newton total unknown if you apply a force then the system will move it may stay at rest or it may move that means state of body will change force apply collision state of body change of a force to ki silo external force an external force can move our body internal force body movement could sling net force current net internal force always zero high always force internal force can move a body only external force movement internal force to the zero zero [Music] very good f dot v power is equals to f dot v that means f v cosine theta is the angle between two vectors who is the internal force of this system a system and internal force attention in this direction away from the body attention same body the potential cuts correctly in this direction that is t literal potential cuts could be in this direction that is t usually the fbd draw kodi fbd draw kodi hey velocity zero second body second body that is m one adhe velocity v one that is ten meter per second tension at a directional tension at a [Music] tension is internal force you can attention internal force so summation of power internal is equals to zero of a force into velocity into cos theta f dot v power it just know power t into v 2 into cos 37 net power plus t 0 nichina velocity nay power ash vena t into v1 into cos 180 is equals to zero angle 37 degree fv cos theta the force into velocity cos intermediate angle 37 it can a velocity a direction a tension or direction angle is 180 degree angle 180 degree angle 180 degree theta 180 degrees fixed fully summation zero monitor 4x5 so v2 into 5 is equals to 10.

[00:52:34]50 by 4 12.5 meter per second [Music] concept slow from the body it attention rotation airport objective tension opposite direction power calculate code of attention like an internal force so internal power nitrogen power due to internal forces is zero displacement angle force sorry force velocity and cos foreign [Applause] foreign [Music] tick tick cancels foreign kenya time starts now done hard panel second the lamp here okay [Music] space drag 2 space rock lego 3 1 2 3 go constant length of rod or string rectangular process 3 at the last process huh length constant [Music] it's a common v1 with a certain angle say 60 degree 60 degree adk at point a b point a active velocity dhc with v2 with v2 say at angle 30 degree 30 degree title along the length huh since length along the length velocity must remain constant along the length the legend along the length velocity constant v1 along the length of velocity v1 cos 60 degree vector a directional velocity v2 along the length of velocity v2 cos 30 along the length velocity constant like you have a v1 cos 60 degree is equals to v2 cos 30 degree about v1 v2 it's this is the concept along the length velocity equals foreign v2 [Music] v2 cos foreign fourth alley v2 is equals to 12.5 come on meter per second isn't that interesting interesting so much fun you see easy it approach will help corporate on a calculation totally like very small so velocity will be constant first processed or the complicated subject [Music] process so there you go [Music] peanut butter oh [Music] literally nature is god nature is physical physics is god plural length constant length of string remains constant the velocity along length on the stream objectives oh net internal power zero change net internal power zero right um okay i check t1 u cos 180 cos 180 plus t1 v cos theta length constantly along the length of string along the length of string though velocity is equals to constant [Music] method b [Music] foreign [Music] foreign foreign action reaction action reaction action reaction action reaction violate cos theta [Music] so this is t1 cos theta t1 sin theta eta t2 cos theta directionally t2 sine theta [Music] d2 sine theta s movement [Music] the lever opponent zero so f net they are for f net along x axis come so we can write summation of power internal zero internal power zero pro system and internal power zero purif what [Music] okay right it's just choking baby just joking opposite direction t 1 u cos 1 80 we cannot e objected t 1 cos t 2 cos v same direction 0 let t 1 cos plus t 2 cos into v into cos 0 again that t 2 o 4 a unit t cos theta into v cos 0 1 plus t at the minus 1 again minus t into u is equals to 0 hello 2t cos theta into v is equals to 2 t u 2 t cos theta into v t u t o 2 t u 2 t cos theta v 2 to u v equals to u by cos theta actually actually v is equals to minus u by cos theta vector vector here the magnitude of that magnitude opposite vulture [Music] me foreign [Music] b hello power concept i feel too happy [Laughter] [Music] foreign oh [Music] or 15 seconds seven six five four three point five three two point nine two point one 2 1.4 1 0.5 0.1 0 time up space draco space drago next here very good minus beta angle between vectors is the angle between their directions math cos pi minus beta minus cos beta sure cos 180 minus beta 180 minus a cos 2 into 90 degree minus beta 2h cos beta con quadrant second quadrant minus of a cos pi minus theta minus cos theta sine pi minus theta sine theta all right by zero likhini oh verify me [Music] foreign new generation try this using length velocity hey [Laughter] [Music] um foreign hey 20 meter per second [Music] velocity component vr cos theta length constant so velocity along string is equals to constant stinger velocity of constant factor v r cos theta is equals to 20 over v r cos thirteen again is equals to twenty cos the cosetic of the volume root three by two very good very good very good vr forty by root three meter per foreign cugo only foreign second find the velocity of block b the airport tension a direction can one divide by that a direction okay a pulley direction [Music] [Laughter] reaction action reaction hello now the question arises from m [Applause] tutti what foreign uh rictor hello [Music] actually fbd or velocity vb vb fbd of a air fbd air fbd auropor net tension 40 for velocity 10 meter per second t 2t 3t a block this 2t this 2t 4t support internalize here internal force such attention tension the summation of power [Music] plus 40 into 10 into cos 180 is equals to zero t t cancel hello vb is equals to [Music] foreign ah 3t vb same direction 3t vb cos 0 40 10 opposite direction 40 10 cos 180 tt cancel over 3 vb cos 0 1 40 cos 180 minus 1 minus 40.

[02:04:13]40 by 3 this is the velocity of vbe rocky foreign what is the velocity of the block b draw this draw this with question with question lovely concept lovely concept which will be taken over dropper it's the same diagram [Music] could be made [Music] m my goodness foreign foreign foreign [Music] a if the rod starts slipping on smooth ground round smooth as you sleep away i sleep capping velocity of b b pointer velocity of a pointer velocity device at 10 meter per second [Music] [Music] foreign [Music] plus n a [Music] scoreboard velocity component squared that is vb cos 37 vb cos 37.

[02:13:14]so m foreign [Music] ah foreign [Music] 53 degree 53 degree at a 90 at a 53 it are vertically opposite of a that is va cos 53 degree keyboard we know velocity along the length of rod remains constant current velocity changes 37 degrees equals to va cos 53 degree volume vb cos 37 monogaro this is 37 eta 53 37 i go to dk 3 then 4 cost 37 into four by five is equals to 10 into three by five settings [Music] foreign foreign [Music] [Applause] system [Music] standards foreign one of my fruity pretty a system um again hello [Music] plus 60 into v2 cos zero degree equals to zero 60 or for a v2 minus differentiating with respect to time time and respect to differentiate corvo differentiation corvoca of s6 a2 is equals to a1 velocity differentiation cool acceleration power kinematics motion 1d again velocity like a differentiate corvo timer respect a dv2 dt velocity differentiate cool acceleration power only six into acceleration equals to a one money a two j acceleration third six times per second square acceleration there is a one this is the next page next page for the key volvo keep h is six a two is equals to a one a two is equals to a one by 6 thermal a2 is equals to 5 by 6 meter per second square it has acceleration of b acceleration of block b b blocker acceleration division on this foreign [Music] m [Music] [Music] support floating pulley with a fixed pulley at a fixed pulley they're floating around floating along oh my goodness oh my goodness oh my goodness indeed floating pulley at the fixed pulley ah same away absolutely not canon attacked a separate string at a separate stream think like please [Music] by doing this by thinking this sound is something [Music] acceleration of biscay me tada