Rotation Motion | Pure Rolling | Rolling, IIT-JEE/NEET #neet #jeemains #rotation #rolling #neet
In this live Lecture I'll discuss Pure Rolling in Rotation motion for JEE Mains and NEET.
Rotation or rotational motion is the circular movement of an object around a central line, known as axis of rotation. A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersecting anywhere inside or outside the figure at a center of rotation.
घूर्णन या घूर्ण गति एक केन्द्रीय रेखा के परितः किसी वस्तु की वृत्तीय गति है। एक समतल आकृति एक लम्बवत् अक्ष के परितः दक्षिणावर्त या वामावर्त दिशा में घूम सकती है, जो घूर्णन के केन्द्र पर आकृति के अन्दर या बाहर कहीं भी प्रतिच्छेद करती है।
Pure rolling is motion of the round object without any slipping or skidding at the point of contact between two bodies. The rolling motion is a combination of translational motion and rotational motion. In pure rolling, the point of contact with the surface has zero velocity.
In metalworking, rolling is a metal forming process in which metal stock is passed through one or more pairs of rolls to reduce the thickness, to make the thickness uniform, and/or to impart a desired mechanical property. The concept is similar to the rolling of dough.
धातुकर्म में, ढ़लाई या रोलिंग धातुओं के रूपान्तरण की वह विधि है जिसमें धातु को दो बेलनाकार रोलरों के बीच से होकर गुजारा जाता है और दोनों रोलर धातु को दबाते हैं।
#srbphysicskota #aksir #aksirphysics #science #physics #yt #rotational_motion #rotation #class11 #jeemain #iitjee #rollingjee #rollingclass11th #purerollingclass11th
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In this live Lecture I'll discuss Pure Rolling in Rotation motion for JEE Mains and NEET.
Rotation or rotational motion is the circular movement of an object around a central line, known as axis of rotation. A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersecting anywhere inside or outside the figure at a center of rotation.
घूर्णन या घूर्ण गति एक केन्द्रीय रेखा के परितः किसी वस्तु की वृत्तीय गति है। एक समतल आकृति एक लम्बवत् अक्ष के परितः दक्षिणावर्त या वामावर्त दिशा में घूम सकती है, जो घूर्णन के केन्द्र पर आकृति के अन्दर या बाहर कहीं भी प्रतिच्छेद करती है।
Pure rolling is motion of the round object without any slipping or skidding at the point of contact between two bodies. The rolling motion is a combination of translational motion and rotational motion. In pure rolling, the point of contact with the surface has zero velocity.
In metalworking, rolling is a metal forming process in which metal stock is passed through one or more pairs of rolls to reduce the thickness, to make the thickness uniform, and/or to impart a desired mechanical property. The concept is similar to the rolling of dough.
धातुकर्म में, ढ़लाई या रोलिंग धातुओं के रूपान्तरण की वह विधि है जिसमें धातु को दो बेलनाकार रोलरों के बीच से होकर गुजारा जाता है और दोनों रोलर धातु को दबाते हैं।
#srbphysicskota #aksir #aksirphysics #science #physics #yt #rotational_motion #rotation #class11 #jeemain #iitjee #rollingjee #rollingclass11th #purerollingclass11th
rotation motion, rotation motion class 11th, rotation motion class 11, rotation motion jee mains, rotation motion neet, rotation motion IIT JEE, rotation motion JEE Main, moment of inertia, rotation, JEE Mains, JEE Main, JEE Mains 2025, NEET, NEET 2025, Physics, Physics JEE Mains, class 11th, 11th, AK Sir, class 11th rotation motion, Pure Rolling in Rotation Motion, Pure Rolling in Rotation Motion class 11th, Pure Rolling in Rotation Motion class11, Rolling in Rotation Motion, Rolling in Rotation Motion class11th, Rolling in Rotation Motion class11,
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LearningTranscript
00:00Hello students, today we are going to tell you about rolling, which is a chapter of rotation motion.
00:15Rolling is a very interesting part of rotation.
00:20Rolling means to roll.
00:22What is rolling?
00:24See, rolling is when the body is rolling.
00:38What is rolling?
00:43How do we understand it?
00:45There are three types of rolling.
00:49Pure rolling, translatory, rotatory.
00:52We will discuss all of them.
00:54Let's start.
00:56Rolling means to roll.
00:59Rolling means to roll.
01:01Let's see how the body rolls.
01:05We are taking a body.
01:12For the new students, we will tell you.
01:17In the previous lecture, we have completed the part of rotation, torque, Newton's second law, moment of inertia.
01:29Now we have come to pure rolling.
01:32Today we will complete pure rolling.
01:35Pure rolling means to roll any body.
01:39We have taken a body.
01:41This is a tape.
01:42We are going to roll it.
01:44This is rolling.
01:47The body is rolling.
01:51We have kept the tape on the hand.
01:56The body is rolling.
01:58This is called rolling.
02:02We have taken a body.
02:06The translation motion and the rotation motion combine to form rolling.
02:17Translation and rotation motion combine to form rolling.
02:22We have taken a body.
02:26First of all, we will see the translation motion.
02:37This is the pure translation motion.
02:40Pure translation motion.
02:51Translation motion means when a body moves on a straight path.
02:56The velocity of all points of the body should be constant.
03:02This is called pure translation motion.
03:14We have considered V1 as the velocity.
03:19The velocity of all points should be V1.
03:28The velocity of all points should be V1.
03:33This motion is called pure translation motion.
03:50After this comes the pure rotation motion.
03:55Pure rotation means when a body rotates about a fixed axis.
04:03This is called pure rotation.
04:05I have told you about pure rotation in the beginning.
04:14Let us explain the pure rotation.
04:17We have taken a body and taped it.
04:20The body rotates about a fixed axis.
04:24This is called pure rotation.
04:27As you have seen, the fan rotates about a fixed axis.
04:33This is called pure rotation.
04:37Hello.
04:40We will take pure rotation here.
04:42We will rotate the center of mass about omega.
04:49When we rotate it, it will have translational velocity.
04:56This is tangential velocity.
04:59This is tangential velocity V2.
05:01We write the radius as R.
05:04The value of V2 will be R omega.
05:07The tangential velocity will also be R omega.
05:22At different points, the tangential velocity will be V2R omega.
05:34We will write R omega here.
05:44We will write R omega here.
05:48There are two types of translation motion and rotation motion.
05:53When we combine these two motions,
05:56the motion that comes out is called rolling.
06:04We are combining these two motions.
06:12We will combine these two motions to make a rolling motion.
06:24I have just shown you.
06:26We have taken a body and taped it.
06:30In this way, the body is doing translation motion in the horizontal direction.
06:36It is also rotating.
06:38This combined motion is called rolling.
06:47When these two motions are combined,
06:50this is pure translation motion and this is pure rotation motion.
06:55When a fixed axis body is rotating,
07:02this is pure rotation motion and this is pure translation motion.
07:06When these two motions are combined,
07:09this is combined motion.
07:11When these two motions are combined,
07:13this is combined motion.
07:17The velocity at the top point is V1 and this is V2.
07:22When these two motions are combined,
07:25the velocity at the top point is V1 plus V2.
07:33The velocity at the center is V1.
07:37In rotation, the velocity at the center is V is equal to R omega.
07:43When the body is rotating outside the center,
07:46the tangential velocity at the center is V is equal to 0 because R is equal to 0.
07:50For the center, V1 is the translation velocity.
07:57The velocity at this point is V1 and this is downward V2.
08:02The resultant of these two will be in this direction.
08:05This is the under root of V1 square plus V2 square.
08:24Here, I have taken some points and numbered them.
08:28This is 1, 2, 3, 4.
08:37We will consider this as P point.
08:39The velocity at these points is V1 and V2.
08:46The resultant of V1 and V2 will be under root V1 square plus V2 square.
08:54When we have combined translation motion and rotation motion,
09:02this will be the combined motion.
09:05There are different conditions for the velocity at this P point.
09:11There are three conditions.
09:14In these three conditions, the final case is called pure rolling.
09:20This is a very good case.
09:23Let us see all three cases.
09:27First, we will see the condition for velocity at P.
09:33We will write Vp.
09:35We do not know this yet.
09:37We have to find it.
09:40This is the condition for velocity at P.
10:06We will find the condition for Vp.
10:09There will be three conditions.
10:11In the first case, when the velocity of translation motion is more than the velocity of rotation.
10:17The first condition is V1 greater than V2.
10:25We have taken translation motion for V1.
10:27What kind of motion did we take?
10:28Translation.
10:29Translation means we have taken a body.
10:32We are moving this body in this way.
10:36We are moving it without rotating it.
10:38This is pure translation motion.
10:41The velocity of pure translation motion is V1.
10:45The velocity of rotation motion is more than V2.
10:50V1 is greater than V2.
10:54The velocity at the bottom will be Vp.
11:08This is the P point.
11:10The velocity at the center will be V1.
11:14The velocity of translation motion is greater than the velocity of rotation.
11:24The velocity of P point will be in the direction of V1.
11:31The value of Vp will be equal to V1 minus V2.
11:38It will be in the forward direction.
11:40It will be in this direction.
11:47This is called forward slipping.
11:50In this case, the body moves forward while slipping.
11:54This is called forward slipping.
12:02This is the possibility of this case.
12:06In physics, it is not enough to read the concept.
12:10It is necessary to understand it.
12:12When will this case happen?
12:14As we have told.
12:16If a body is moving in translation and rotation motion.
12:26In that case, if the velocity of rotation is reduced and translation is learned.
12:35We are giving an example.
12:37We are driving a car.
12:43The car is moving on the road.
12:45If we apply the brake suddenly, the rotation motion will be reduced.
12:53But if the car is moving at high speed, it will have good translation motion.
12:59In that condition, the tires slip on the road.
13:04You have to focus for that.
13:08In this case, the translational velocity will be more and the rotation will be less.
13:17This is called forward slipping.
13:20The body will move forward while slipping.
13:23This is the first case.
13:28The second case is
13:32V2 greater than V1
13:42The velocity of rotation is more than the translation.
13:50The translational velocity will be less than the rotation.
13:57The body will rotate at high speed.
14:00When the body rotates at high speed, backward slipping will occur.
14:05Like this.
14:11The center of mass velocity will be V1.
14:23Here, it will slip at the bottom.
14:29We took the P point as the value of Vp.
14:43V2 minus V1 will slip backward at the P point.
14:48The body will move forward.
14:50It is not difficult to understand this.
14:55You have to put extra effort to understand this.
15:01You have to see when this happens.
15:04If you have seen it, it is very good.
15:06Let's take an example.
15:12A car is stuck in mud.
15:15When the car is stuck in mud, the tires rotate very fast.
15:21When the car is stuck in mud, the tires rotate very fast.
15:24The car slips backward.
15:27The car moves forward slowly.
15:32But the rotation of the tires is very fast.
15:35The car moves forward slowly.
15:40But the rotation of the tires is very fast.
15:42This is called backward slipping.
15:51This is called backward slipping.
16:01The velocity at the P point will be in the backward direction.
16:06It will be equal to V2 minus V1.
16:09We found the value of V2.
16:11It will be equal to R omega.
16:13We took the omega angular velocity.
16:16Now comes the third case.
16:23When V1 is equal to V2.
16:33When V1 is equal to V2.
16:36This is called pure rolling.
16:40This is called pure rolling.
16:43The value of V1 will be zero.
16:47This is called pure rolling.
16:50It sounds strange.
16:58How will the velocity at the bottom be zero?
17:01The body will move forward.
17:04How will the velocity at the bottom be zero?
17:06We will show how it will be zero.
17:15We have taken a disc.
17:22We are going to roll it on the surface.
17:26The velocity at the center is V1.
17:32At this point, due to it's translational motion,
17:35It will get velocity in V1 forward direction.
17:40And due to it's rotation, it will get velocity in V2 backward direction.
17:44V1 is cured due to translation motion.
17:49We are taking translation motion of the body.
17:55This is translation motion.
17:57This is rotation motion.
18:00motion is like this, it is a pure rotation, when we rotate a fixed axis body, it is a pure rotation,
18:09now if you see in pure rotation, the velocity at the bottom is backward, see the velocity of this point
18:17will be backward and in pure translation it is forward, now both are equal and opposite,
18:23so the velocity at the bottom point will be cancelled, so the value of Vp will be 0,
18:31the velocity at the P point will be 0, this is called pure rolling,
18:41see here when we move the body without slipping, this is called pure rolling,
18:56see this is the case of pure rolling, the velocity at the bottom, at the P point where the surface is in contact with the body,
19:06the velocity is 0 and the velocity at the center is V1 and V1 is equal to V2, we can write it as V0,
19:16it does not make any difference, we have accepted it, and the velocity at the top point will be V1 plus V2,
19:25this will be 2V0, see in pure rolling the most important point is,
19:32the velocity at the bottom point is 0, the velocity at the center is V0,
19:48the velocity at the top point is double of the center and mass,
19:56let us take this as P and this as Q point, and this is center and mass,
20:04so Vcm, if this is V0, then the velocity at the top point will be 2 times of Vcm,
20:15this will happen in pure rolling only, if this is pure rolling, then the velocity at the bottom will be 0,
20:22the velocity at the center and mass is just double of the top point,
20:27now the point which we have taken here, we will write it as V0,
20:35if this is V0, then its resultant will come in this direction, V0 root 2,
20:41similarly it will come here also, this is V0, it will be V0 in this direction,
20:51this will be V0 and this will be V0 root 2,
20:56see this is pure rolling, here we have considered only the velocity,
21:02we have told about the velocity, now we will tell about the acceleration,
21:08acceleration in pure rolling,
21:23see how we will see the acceleration in pure rolling,
21:32so the translation motion, rotation motion, and when we will combine those two motions,
21:39then the final resultant will be pure rolling,
21:44the condition for pure rolling is,
22:02see here we have three diagrams,
22:22so first of all we will see pure translation motion,
22:32see here we will see pure translation motion,
22:52see in pure translation motion, when translation motion is there,
22:58so before this when we have told about the velocity,
23:00so the velocity of all the points was same,
23:03so here the acceleration of all the points will be same,
23:07the acceleration of center of mass will be same,
23:12the acceleration of all the points of the whole body will be same,
23:15we are considering A0,
23:22because we are going to tell about pure rolling,
23:24see like this,
23:26the acceleration of all the points will be same,
23:32now when we will see pure rotation,
23:36so in pure rotation when the acceleration will be there,
23:39so here the tangential acceleration and angular acceleration will be there,
23:43so here the body will rotate,
23:48this is pure rotation,
23:54in pure rotation the body will rotate with the center of mass about alpha angular velocity,
24:07this is alpha angular acceleration,
24:11so here this tangential acceleration will be A0,
24:20here in backward direction tangential acceleration will be A0,
24:25and here the top will be A0,
24:29the value of A0 will be equal to r alpha,
24:35r is the radius,
24:37A0 means the tangential acceleration here will be equal to the translation motion acceleration,
24:47because we have to do pure rolling,
24:49like we have taken the velocity V1 is equal to V2,
24:53here the tangential acceleration will be equal to the translation acceleration,
24:59now when we will combine these two,
25:02this will be pure rolling,
25:08here the acceleration at the top point will be 2A0,
25:14the acceleration at the center of mass will be A0,
25:18and the acceleration at the P point will be 0,
25:34so this is pure rolling,
25:36there is no problem in this,
25:40now see when a body rolls on a rough surface,
26:09when a body rolls on a rough surface,
26:14so in that condition a friction is applied which is called rolling friction,
26:19now we will tell you about rolling friction,
26:32see rolling friction is a conservative friction force,
26:36friction is non-conservative,
26:40but rolling friction is a conservative force,
26:52rolling friction is a conservative force,
26:55now when a body rolls on a rough surface,
26:57we have to find out in which direction friction will be applied,
27:02direction of rolling friction,
27:07it is a very difficult task,
27:28direction of
27:36rolling
27:38friction
28:06direction of
28:08rolling
28:10friction
29:06then the direction of predicted direction of
29:15direction of f r rolling friction is correct
29:23consider any direction of rolling friction
29:29consider any direction of rolling friction
29:35you don't know whether it is correct or not
29:39if after solving the problem the value of rolling friction is positive
29:43then your assumption will be correct
29:47if it is negative
29:51then there is no problem
29:55the predicted direction will be incorrect
29:59then the predicted direction
30:11of f r rolling friction is
30:15incorrect
30:19the predicted direction will be incorrect
30:23the correct direction will be reverse of the predicted direction
30:27and the magnitude will be same
30:31there will be no change in magnitude
30:35and the
30:39correct direction
30:43of
30:51reverse of
30:55predicted direction
31:07with the same magnitude
31:11with the same magnitude
31:23if we have considered any direction in rolling friction
31:27the value of rolling friction comes to positive
31:31then as set by the predicted direction will be correct
31:35if the value of direction comes to negative
31:39will be incorrect and the correct direction will be reversed.
31:44As you can see here, we have considered rolling friction in backward direction.
31:50Now if the value of rolling friction is positive, then this direction is correct.
31:55But if it is negative, then this direction of rolling friction will not be correct,
32:02it will be incorrect, magnitude will remain the same, we just have to reverse the direction.
32:08Now see, what is the magnitude of rolling friction?
32:25The value of rolling friction is minimum value is 0 and maximum value FR will be limiting.
32:37This is the magnitude of rolling friction, minimum value of rolling friction will be 0
32:43and maximum value of rolling friction will be FR limiting.
32:48So this is the range for rolling friction.
32:52Now the formula for limiting rolling friction is like FS limiting.
32:59FR limiting is equal to mu R into N.
33:05Mu R is the coefficient of rolling friction.
33:18Coefficient of rolling friction.
33:30Now we have studied static friction, kinetic friction and rolling friction, three frictions.
33:41The value of mu S is the maximum coefficient of static friction.
33:49Mu K is the kinetic friction coefficient.
33:53And the minimum value is the coefficient of rolling friction.
33:59So this is their relation.
34:03Mu S is the coefficient of static friction.
34:09Mu K is the coefficient of kinetic friction.
34:12The value of mu S is the coefficient of static friction.
34:16And the coefficient of rolling friction will be less than mu K.
34:20Now let us discuss a question on this.
35:23Here we have taken two blocks, one is the bridge and the other is the mass.
35:51We take the mass of 2M and this is the bridge and its mass is M radius R.
35:59Here the friction will be on the bridge and this is the rough surface.
36:35We take the mass of 2M and this is the radius of the bridge and its mass is 2M and its radius is R.
36:54We have connected the block from its center.
36:59This is the disk and this is the bridge.
37:08Now we will find the acceleration and tension of the two blocks.
37:16And the most important thing is that we will find the rolling friction.
37:20What will we find?
37:21Rolling friction.
37:22We can consider the direction of the rolling friction as per our convenience.
37:32We are considering the direction of the rolling friction to be backward.
37:40Now see here there are two motions in rolling, one is the translation motion and the other is the rotation motion.
37:52We will consider the acceleration of this as A and its acceleration will also be A of the center and mass.
38:14First we will make the FVD of the block and then the pulley.
38:19And here the tension will be different.
38:22Here T1 and here T2 tension will be there.
38:27It is the same string but here we are taking both the mass and friction in the pulley.
38:34That is why the tension is different.
38:37In the beginning when I taught the pulley in NLM, I cleared this concept that if there is both mass and friction in the pulley, then T1 and T2 are not equal.
38:52Now we will need that.
38:54So here we will first draw the FVD or FVD Free Body Diagram of Capital M.
39:08So the motion of Capital M is the translation motion.
39:12MG will be downward and T1 will be upward and its acceleration will be A downward.
39:19So from here the equation will be MG minus T1 is equal to MA.
39:27After this we will make the FVD of the pulley.
39:31The pulley is rotating.
39:33It will be the pure rotation motion.
39:37FVD, Free Body Diagram of Pulley, Pure Rotation.
40:07Here we will take its pure rotation motion.
40:20We will make a diagram.
40:24In its pure rotation motion, MG will be at the center of mass.
40:30MG will be downward.
40:33Here T1 will be here.
40:36Here T2 will be here.
40:38Here is the normalization.
40:41It will rotate with the angular acceleration of alpha.
40:50We will take the moment of inertia of angular acceleration as I.
40:55Here the torque of MG and normal action will be zero about the center of the pulley.
41:07Tau MG about C will be zero because its line of action is passing from the center.
41:14The torque of T1 will be clockwise and T2 will be anticlockwise.
41:21Tau T1 into R will be clockwise and Tau T2 into R will be anticlockwise.
41:32The torque of T1 minus T2 will be T1R minus T2R is equal to I alpha.
41:51The moment of inertia of I disc will be MR square by 2 and alpha value will be AYR.
42:04T1 minus T2 is equal to MA by 2.
42:09This will be the second equation.
42:13We will have to consider two motions of the disc.
42:20One is pure translation motion and the other is pure rotation motion.
42:35First of all, we will make the pure translation motion.
42:39Pure translation motion.
42:49Pure translation motion.
43:09We have taken rolling friction on the back side and this will be the acceleration.
43:17We have taken mass side as 2m.
43:20Yes, mass is 2m.
43:22We will take mass as 2m.
43:25This is 2m.
43:27The value of N will be equal to 2MG.
43:34T2 minus AFR rolling friction is equal to 2MA.
43:42This will be the third equation.
43:46We have made three equations.
43:48Now we will make one more equation.
43:52When we draw the FBD of pure rotation motion of the disc, we will get one more equation.
44:02We will solve this equation.
44:04FBD of disc in pure rotation motion.
44:18This was our diagram.
44:20We have to see the pure rotation motion of the disc of 2m mass.
44:28If the acceleration of the center of mass is in the direction of A, then the acceleration of the top point will be 2A.
44:38The tangential acceleration will be equal to 1A.
44:50We will draw the FBD of disc.
44:58We will draw the FBD of disc.
45:10We will show the force applied on the disc for pure rotation motion.
45:16MG will be downward.
45:18Normal will be upward.
45:20Tension T will be in the center.
45:24Rolling friction will be at the bottom.
45:26This will be the force applied on this disc.
45:30Now this is the force.
45:32The angular acceleration of this will be alpha.
45:34The moment of inertia is 2 m mass radius r.
45:36The center of mass is about tangential acceleration.
45:44The center of mass is about tangential acceleration.
45:46mask about a tangential acceleration is a mix up there 80 a k equal over center
45:55of mass care of the key to normal a son cut off over zero because normal
46:01reaction center say past garage the line of action is a center say past
46:07career to perpendicular distance zero g or perpendicular distance figure line of
46:14action say zero atom net or the zero jagani normal a son cut off hero hogar
46:21enter cabal tension we enter play like a center says TV line of action past
46:28Karegi or tension Kavi talk to zero hogar or mg Kavi talk to zero hogar
46:39therefore there for rolling friction cut or to zero may he hogar
46:46yeah far into perpendicular distance are or a ski direction joe Ig inside Ig
46:55give our cross F karte hain direction inside a jaggi
47:03you
47:08yes
47:11love from an IT Surat okay
47:19the key in it or forget down it is your hotel I alpha K equal or the yoga yeah
47:28into our IQ value is come moment of inertia of the cylindrical excess about
47:35mr square by 2 that the MQ value a 2m r square by 2 or alpha K value will be e
47:45upon r k equal
47:48you
47:50we are pencil or jagat to say to cancel or jagat yeah for rolling friction key
47:57value I mean to a key a fourth equation
48:07yet I request and he Robin savvy question code a km add
48:14a
48:16question I am
48:18first
48:20second
48:22third
48:24fourth
48:26first equation
48:28mg minus
48:30even a left side
48:32mg minus
48:34even
48:36question
48:38the question
48:40first equation
48:42a
48:44mg minus
48:46even a
48:48second
48:50even
48:52even
48:54even
48:56even
48:58even
49:00even
49:02even
49:04even
49:06even
49:08even
49:10plus
49:12first
49:14second
49:16by
49:18two
49:20four
49:22four
49:24four
49:26four
49:28four
49:30four
49:32four
49:34four
49:36four
49:38four
49:40four
49:42add
49:44add
49:46problem
49:48problem
49:50solve
49:52sp
49:54sp
49:56sp
49:58sp
50:00this is cancelled, so from here we will get mg in the left side
50:04and here the acceleration is constant and a is common
50:09and here m plus m, 2m, 2m, 3m
50:13and in 3m, m by 2 means 3.5, that is 7
50:18m by 2 will come
50:21no, something is wrong
50:24it will not be 7, it will be 9
50:28ok, this ma, ma, 2ma and 2ma is 4ma
50:33and in this we will add half ma
50:36then 4.5 means 9ma by 2 will be there
50:41and here m by m will be cancelled
50:44the value of a will be 2gy9
50:50now the acceleration has come
50:52we just said about the rolling friction
50:56the rolling friction is correct or not
51:00so here the last equation was 4th
51:05if we put the value of a
51:08y equation 4th
51:14the rolling friction will be positive
51:17the value of fr, m into a is equal to
51:21and m is m, the value of a is 2gy9
51:26so this will be 2mg by 9
51:32this will be the rolling friction
51:34and the value of rolling friction is positive
51:38so the direction we considered
51:42the direction we assumed for rolling friction is correct
51:45because it is very easy to do rolling friction
51:49for rolling, rolling is not difficult
51:51it is very easy, we just have to understand its concept
51:55what is there in rolling, we have to consider two parts
51:58now when we study NLM, we consider only translation motion
52:04and in circular motion
52:07we do not consider only circular motion
52:12before this when we studied rotation, we considered only rotation
52:17so this is the starting part of rotation motion
52:20now here we have to consider rotation along with translation motion
52:26both have combined motion, that is rolling motion
52:30we have to work hard to understand this
52:40see, we have told a lot in today's lecture
52:43and we will upload its pdf on our telegram channel
52:49on srv physics quota
52:51you can see its pdf on that
52:54you can also download
52:56so we will complete today's lecture here
52:59because in rotation, in pure rolling
53:02the question is little long
53:04so we will discuss more questions on this in next time
53:09we will complete today's lecture here
53:12ok