Laws of motion/Grade-11/JEE/NEET/Physics

Añadido: 2026-05-24

[00:01:59]Mhm.

[00:03:54]>> Mhm.

[00:07:06]>> Hello students.

[00:07:09]Welcome to the student the brand.

[00:07:14]Hello students. Welcome to the student the brand. This is your today topic is laws of motion. Okay? So, laws of motion. So, let's discuss about it.

[00:07:26]Laws of motion.

[00:07:30]Laws of motion.

[00:07:40]Okay.

[00:07:41]So, today topic is laws of motion.

[00:07:46]Understood or not?

[00:07:49]So, in this class, we'll discuss about First point is inertia.

[00:07:57]So, what is the meaning of inertia? What exactly the inertia?

[00:08:02]Inertia is nothing but So, inability of the body to start or to change its position.

[00:08:15]So, body is not able to change its position unless until external force acting on it.

[00:08:22]The body is not able to change its position by itself. Okay? So, the body couldn't able to Okay. So, the body is not able to change its position.

[00:08:41]Change its position. Right? So, without any external force acting on it. Without any external force acting on it. So, that is called inertia. So, there are three types of inertia. So, one is inertia of rest, inertia motion.

[00:09:00]So, first one is inertia inertia. So, A rest.

[00:09:09]Inertia of rest.

[00:09:12]Inertia of rest and B is inertia motion.

[00:09:17]And D is inertia A B C.

[00:09:22]Inertia of direction.

[00:09:27]Okay?

[00:09:28]So, what is inertia?

[00:09:35]Inertia is nothing but so unable to change its position by its own.

[00:09:42]Right? So, point number one, inertia of rest, inertia of motion, inertia of direction.

[00:09:48]So, inertia of rest.

[00:09:50]So, one example I'll tell.

[00:09:53]So, if you beat the carpet with a stick, okay, if you beat the carpet with a stick, the dust particles will fall down.

[00:10:04]The dust particles will fall down. Okay, the carpet comes under motion.

[00:10:10]And if you shake the branches of the tree, if you shake the branches of the tree, okay, so fruits will fall down. Fruits will fall down.

[00:10:24]Then, so branches of the tree comes under motion.

[00:10:28]So, that is one example.

[00:10:30]And one more example, so take a glass of water, place the paper on it, place the coin over it, and drag the paper. So, the coin will fall down.

[00:10:42]That is one example. And one more example, okay?

[00:10:48]So, one more example you can see.

[00:10:53]So, carrom coins, if you hit the bottom of the coin, so that coin will move forward, remaining coins stay same place, okay? So, these are all example for inertia of rest. Okay? Unless external force acting on it, the body stays in the same state.

[00:11:13]State of rest. And coming to state of motion.

[00:11:18]So, if you on the fan, if you switched on the fan, the fan continuously rotating. The fan continuously rotating. Understood or not? So, once once you off the fan, still it continues. Still it continues. Even though you switched off the fan, so the fan will continuous its motion due to inertia of motion. And uh if you observe the athlete, okay, so the person who is taking long jump especially, so he will move backward to gain that inertia of motion. Okay? So, he will go back and uh run from certain distance. So, then after that after running certain distance, he'll get that momentum, he'll get that motion, then he'll continuous he'll continuous in the air until certain distance. So, due to inertia of motion. And one more example we can say inertia of direction.

[00:12:24]So, I'll tell inertia of direction. So, the person is getting down from the running bus. Okay? If the person is getting down from the running bus, okay, so what happens? He has to move in the same direction. So, in the direction of the bus motion. So, he has to move until certain distance, then only he can able to stop himself. Otherwise, so immediately if you want to immediately want to stop himself, so he couldn't able to do that. So, he'll fall and roll.

[00:12:57]Right? So, due to inertia of direction.

[00:13:01]And one more thing, if you take a stone tied to the thread and whirl and it rotate in a circular motion and leave, so the stone will move along the tangential direction. The stone will move along the tangential direction due to inertia of direction. And one more thing, so during rainy season during rainy season, so if the person is bicycling, so back side wheel you can observe the water droplet will move along the tangential direction. Along the tangential direction. Understood or not? Until unless if you apply force on it, the body continuously stays in the same state. Either it is state of rest or state of motion, state of direction, okay? Depends. Understood or not? I hope it is very clear. So, these are all the points about inertia. About inertia. I hope it is very clear.

[00:13:58]Understood or not? Coming to the next one.

[00:14:01]Next one is forces. There are two types of forces.

[00:14:06]One is contact force.

[00:14:10]Contact force.

[00:14:13]Contact force. Second one is non-contact force.

[00:14:19]Non-contact force.

[00:14:23]Non-contact forces, contact forces.

[00:14:28]So, coming to the contact forces.

[00:14:31]Contact force example.

[00:14:33]Okay? Contact force example. So, if the bodies are in contact, the force will act. So, when the two bodies are in contact, then the force will act.

[00:14:43]Example, so we can take frictional force, muscular force, tensional force, spring force. Okay? These are all contact forces. So, when we are when we are walking on the ground, when we are walking on the ground, so our motion will be forward, the friction will opposes our motion.

[00:15:06]So, what exactly the friction? The interlocking of irregularities, okay?

[00:15:11]So, there is no perfect smooth surface.

[00:15:14]There must be some irregularities, okay?

[00:15:17]So, between one surface to another surface, so the interlocking of irregularities, interlocking of irregularities is known as So, it causes interlocking of irregularities causes friction.

[00:15:32]Okay? So, frictional force it opposes the motion of our body uh motion of the body. Uh when we are moving, so motion So, it opposes as when the body is moving, it opposes the motion of the body. Like if So, best example, if you throw the ball, okay? So, until certain distance it will travel and it will stop automatically. So, anyone is applying force on it? No. So, the friction between the uh uh ground and ball, ground and object. So, due to that reason the ball is stopping until until when?

[00:16:10]Uh if you external force is applied, so immediately it will stop. Without external force, until certain distance it will move, then it will stop.

[00:16:18]Understood or not? So, coming to the next one, muscular force. So, we are lifting the object, right? We are lifting the heavy object. We are lifting the heavy object.

[00:16:29]So, with the muscular force only we can able to lift. So, if you want to displace the bench, if you want to drag the bench, if you want to uh move the chair, okay? By using our muscles, we can able to change the position of an object, then that force is called muscular force. And coming to the next one, so we can take uh uh friction, uh muscular force, tensional force. When you the object is suspended to the wall or suspended to the Okay? So, ceiling, then tension will be there in the thread. Okay? So, these are all examples for contact forces. And coming to the non-contact forces. So, non-contact force example, electrostatic force, gravitational force, magnetic force. Okay? So, coming to the electron like a gravitational force. So if you leave the object, if you drop the object, always the object moves towards its earth's center. Understood or not?

[00:17:31]Always the body moves towards its earth's center. Understood or not?

[00:17:37]Yes. So without contact, the force is acting on the body. Without contact, the force is acting on the body, so that is gravitational force. Coming to the magnetic force. Okay, magnetic force.

[00:17:53]So what is magnetic force? So north pole north pole repel or attract? Repel. North pole south pole attract. South pole north pole attract. South pole south pole repel. So here you need to understand one thing, two dissimilar poles two dissimilar poles will repel each other.

[00:18:15]Two similar poles Two dissimilar poles attract. North pole south pole attract. South pole north pole attract. North pole north pole repel. South pole south pole repel. So two similar poles repel each other. Two dissimilar poles attract each other.

[00:18:32]Understood? Two different poles, best example we can say north pole south pole attract each other. South pole south pole repel. North pole north pole repel.

[00:18:41]Understood or not? That is about magnetic force. Coming to the electrostatic force. What is that?

[00:18:48]Electrostatic force. So if you take a comb and comb it, if you take a comb and comb it and take near to the piece of papers, if you take a comb and comb it, take near to the piece of papers, then what happens? So piece of papers will be attracted or getting attracted towards the comb because of electrostatic force. And then take the balloon, rub it and take near to the uncharged balloon. Automatically it's getting attracted due to electrostatic force. So, by certain distance only the force will act. The force will act. Understood or not? So, these are all examples for non-contact forces. Non-contact forces.

[00:19:34]And coming to the next one, momentum.

[00:19:37]Momentum.

[00:19:39]So, momentum is nothing but mass into velocity.

[00:19:43]Momentum is nothing but Momentum is nothing but mass into velocity. Mass into velocity. Understood or not? Mass into velocity. So, P bar equal to P bar equal to M into V bar. M into V bar. So, P bar is a vector quantity. P bar is a vector quantity.

[00:20:04]Understood or not? P bar is nothing but momentum. P bar is nothing but momentum.

[00:20:08]Understood or not? So, law of conservation of linear momentum. What is the law of conservation of linear momentum? So, momentum before collision equal to momentum after collision. So, like a two bodies are there. So, two bodies are going to collide each other.

[00:20:23]So, going to hit each other. What happens? So, that time so I'll I'm drawing.

[00:20:29]So, two bodies. Just observe here.

[00:20:37]Okay. So, here you can see.

[00:20:40]So, I'm taking the two bodies here.

[00:20:44]M1 U1 M2 U2. So, these two bodies are collide each other.

[00:20:55]M1 M2 So, after after collision after collision bodies are moving with a different velocities. After collision bodies are moving with a different velocities. So, here you can see m1v1 So, then m2 v2.

[00:21:18]Understood or not? m1v1 and m2v2. Is it clear? Now, you can see m1u1 plus m2u2 equal to m1v1 plus m2v2.

[00:21:35]Is it clear or not?

[00:21:36]Is it clear or not? I hope it is very clear.

[00:21:39]I hope it is very clear. Just check once.

[00:21:43]So, momentum before collision equal to momentum after collision. Momentum before collision equal to momentum after collision. Is it clear or not? So, coming to the next one, law of conservation of kinetic energy. So, kinetic energy before before collision equal to kinetic energy after collision.

[00:22:02]So, best example So, uh like uh what is law of conservation of energy? What is law of conservation of energy? Energy neither be created nor be destroyed.

[00:22:14]Energy neither be created nor be destroyed, but it changes from one form to another form. Energy neither be created nor be destroyed, but it changes from one form to another form. Okay, so that is called law of conservation of energy. So, here we are talking of law of conservation of momentum. So, momentum before collision equal to momentum after collision. So, m1u1 plus m2u2 equal to m1v1 plus m2v2. Is it clear or not? So, coming to law of conservation of kinetic energy. So, kinetic energy before collision equal to kinetic energy after collision. Kinetic energy before collision equal to kinetic energy after a Understood or not? So, I hope it is very clear. I hope it is very clear. Right?

[00:23:06]So, now we'll see Next one, impulse.

[00:23:20]Impulse. Impulse is nothing but large force acting a small interval of time.

[00:23:26]Large force acting in a small interval of time, that is impulsive force.

[00:23:31]So, here you can see So, I equal to f into t. I equal to f into t.

[00:23:44]Understood or not? I equal to f into t.

[00:23:47]So, large force acting in a small interval of time. Large force acting a small interval of time. Understood or not? So, you're taking the So, you can see the batsman, he will hit the ball.

[00:24:00]So, by using maximum force in a So, within a short interval of time. So, in very less time, the batsman will hit the ball. Yes or no? So, large force acting a small interval of time, that is called impulsive force. Impulsive force. Is it clear or not? So, now you can see I equal to this is also known as change in momentum. This is also known as change in momentum. That is I equal to mv minus mu. I equal to mv minus mu. Understood or not? Yes. So, now we'll discuss about So, Newton's laws. Newton's laws.

[00:24:44]Understood or not?

[00:24:50]Newton's laws.

[00:24:53]Newton's laws. Okay, so those are First one is Uh first law So coming to the second law And coming to third law, that's enough.

[00:25:10]Third law.

[00:25:14]Okay, so Newton's first law, second law, third law.

[00:25:18]Newton's first law, second law third law.

[00:25:32]Newton's first law, second law, third law. So what is first law? So Newton's first law describes about inertia. Newton's first law describes about inertia, okay? So inertia we discussed So unless external force acting on the object, the object is not moving from its position. Okay, so there are three types inertia of rest, inertia of motion, inertia of direction. Understood or not? So coming to the Newton's second law. Newton's second law. The net external force acting on the object is equal to mass into acceleration. Mass into acceleration. The net external force The net external force acting on the object, okay? So here you can see The net external force The net external force acting on the object So that is F external equal to mass into acceleration. So how you got this one?

[00:26:27]That is So F is directly proportional to rate of change in momentum. Rate of change in momentum. Net external force is equal to rate of change in momentum.

[00:26:39]So F is directly proportional to MV minus MU by T. So F equal to K into MV minus MU by T. K F equal to F equal to K into MV minus MU by T. Understood or not? So here you can see F I'm taking common.

[00:27:00]M I'm taking common. So here you can see F equal to K into M.

[00:27:07]So V minus U by T is what?

[00:27:11]V minus U by T is acceleration. V minus U by T is the acceleration. Okay, so the rate of change in momentum. Rate of change in momentum. Understood or not?

[00:27:22]So K equal to one. So then F equal to MA.

[00:27:29]So that is net external force acting on the body is equal to mass into acceleration. Mass into acceleration. Is it clear or not? So I hope it is very clear. So coming to the next one. So next we will discuss about Newton's third law. So for every action there is equal and opposite reaction. For every action there is equal and opposite reaction. If you are throwing the object, if you are throwing the object, okay? So object is going to hit the wall. Again it coming to coming to us, right? Coming to us. So understood or not? So that is Newton's third law. Newton's third law.

[00:28:06]And one more thing. So when we are in the Okay, so I hope it is very clear. So this is about the Newton's first law, second law, and third law. So coming to the next one is uh Lami's theorem.

[00:28:50]Okay?

[00:29:01]So, we are now we are going to discuss about Lame's theorem.

[00:29:06]Lame's theorem.

[00:29:08]Right?

[00:29:10]Yes.

[00:29:11]So, here you can see force F1 F2 F3 F1 to F1 alpha, opposite to F3 beta, opposite to F3 gamma.

[00:29:35]Understood or not?

[00:29:37]So, I hope it is very clear.

[00:29:39]Now, F1 by sin alpha F1 by sin alpha F2 by sin beta and F3 by sin gamma.

[00:29:56]Okay?

[00:29:57]So, F1 by sin alpha, F2 by sin beta, F3 by sin gamma. Is it clear or not?

[00:30:04]Yes. So, next one we will discuss about weight. Okay? So, weight is there, tension is there.

[00:30:14]So, when we are in lift the weight is acting downward direction reaction force is acting upward direction. Yes or no?

[00:30:23]When we are in the lift when we are in the lift Okay? So, let's discuss about it.

[00:30:34]So, see here.

[00:30:37]When we are in the lift, so I'm taking here like So, reaction force is upward.

[00:30:49]Tension is acting downward direction.

[00:30:52]Reaction force is upward. Tension is acting downward direction.

[00:30:57]Yes or no?

[00:30:58]Yes. So, if the body is moving with the constant velocity if the body is moving with the constant velocity or First one is if the body is moving with a constant velocity or the body is at rest or lift at rest.

[00:31:15]So, lift is at rest. Okay? So, now we can see R equal to So, lift is moving with a constant velocity or lift is at rest.

[00:31:26]So, R equal to mg.

[00:31:29]R equal to mg. So, next one is So, lift is moving upward direction with acceleration A.

[00:31:46]Okay?

[00:31:52]Lift is moving upward direction.

[00:31:55]Lift is moving upward direction with acceleration A.

[00:31:59]Is it clear or not? Now, you can see a So, which force is greater? Reaction R1 is greater, right? Because along that direction acceleration is there.

[00:32:12]Lift is moving upward direction. So, acceleration R1 is greater than So, R1 is greater than weight of the object. R1 is greater than the weight of the object. So, R1 minus mg equal to ma.

[00:32:28]Then R1 equal to m you are taking common g plus a.

[00:32:35]Okay? So, g plus a. So, this is one. And coming to the next one, coming to the next one. So, if the lift is moving downward direction, if the lift is moving downward direction with the acceleration A, so that time what happens? So, lift is moving downward direction.

[00:33:17]Okay, so here you can see so reaction force R mg is acting downward direction R2 mg.

[00:33:33]R2 mg. Is it clear or not?

[00:33:36]Now, lift is moving downward direction.

[00:33:41]Lift is moving downward direction, right?

[00:33:46]So, now mg is greater minus R2 equal to ma.

[00:33:54]Then, mg minus ma equal to R2.

[00:34:02]Right? So, now you can take R2 equal to m you're taking common g minus a.

[00:34:13]Lift is moving downward direction. Lift is moving downward direction, so weight is greater than the reaction force.

[00:34:21]Weight is greater than the reaction force. That's why mg minus R2 equal to ma. So, mg minus ma equal to R2. So, R2 equal to mg are taking g minus a.

[00:34:34]So, we can understand when the lift is moving upward direction, we feel somewhat weight.

[00:34:41]Okay? So, when you are lifting when lift is moving downward direction, we feel somewhat weightless.

[00:34:48]Okay? So, then compared to the normal weight.

[00:34:52]Is it clear?

[00:34:58]So, next one, so I'll just discuss about friction.

[00:35:04]Friction, friction friction, friction, friction, friction.

[00:35:16]Friction.

[00:35:19]So, what is friction?

[00:35:22]So, friction is also a force.

[00:35:26]Friction is also a force which opposes the relative motion between two objects.

[00:35:35]Okay? So, when the object is moving on another object, so it opposes the motion of an object. That is called a friction.

[00:35:45]So, friction, there are three types. Friction, friction, friction.

[00:35:55]First one is static friction.

[00:36:01]First one is static friction.

[00:36:03]Okay? Static friction.

[00:36:12]So, coming to the next one is limiting friction.

[00:36:21]Static friction, limiting friction.

[00:36:27]Limiting friction.

[00:36:36]Coming to third one.

[00:36:38]Kinetic friction.

[00:36:42]Kinetic friction.

[00:36:50]So in kinetic friction, there are two again. One is sliding friction.

[00:36:56]A is sliding.

[00:37:01]And a B is rolling.

[00:37:08]So static friction.

[00:37:10]Static friction is a self-adjusting friction.

[00:37:17]Static friction is a self-adjusting friction.

[00:37:21]So best example. So when you place a book on the table, initially, when the book is on rest, okay, book is at book is on the table, it is at rest. So the friction will be there.

[00:37:35]And one more thing, initially, if you want to drag the table, okay. So what happens? So it's required more force to displace the object. Because bodies are at rest having static friction. Okay. So at static friction, friction will be more.

[00:37:54]Friction will be more compared to the remaining. What are those? Limiting friction and actually, limiting friction is the maximum value of static friction.

[00:38:04]Limiting friction is the maximum of static friction. Example, so I am applying force, okay, on the table.

[00:38:12]So I'm keep on Okay, I'm keep on applying force. Applying force. Applying force. Applying force. Not coming. So body is not coming. Body is not coming.

[00:38:22]Again, you are applying. Again, you are applying. Still, it is not coming. So, you are applying more force. More force.

[00:38:28]More force.

[00:38:30]Set a maximum force you applied. Okay, if you apply maximum force, the body is ready to move.

[00:38:41]So, the body is ready to move. That is called at that time, the friction will be there. That is a limiting friction.

[00:38:49]The maximum value of static friction.

[00:38:52]Maximum value of static friction.

[00:38:54]Understood or not? At that point, the body is ready to move. At that point, the body is ready to move. Understood or not? Once again, you are applying force.

[00:39:04]Force applying applying applying force applying force applying force applying Done. Done. Done. Done. Not coming. Not coming. Again, you are applying. Coming.

[00:39:12]Not Not coming. Applying Not coming.

[00:39:14]Applying Not coming. So, so it is not like this. We have to apply more force.

[00:39:21]So, applying You are applying maximum force. Then, the body is ready to The body is ready to start. So, that time So, that is a maximum value of static friction. So, after that, if you apply force, then immediately it start moving.

[00:39:39]Understood or not? Then, once it is start moving, it comes under kinetic friction. So, in that, one is sliding friction, another one is rolling friction. Where is sliding friction? So, best example of windows. If you Did you observe windows?

[00:39:52]Did you observe windows? Understood or not? So, window is sliding over another one. Yes or no? So, that is sliding friction. So, in any constant any motion in a fixed position, so one window will be sliding over another surface. Slide Window will be sliding on another surface. That is sliding friction. So, and one more thing, kinetic rolling friction. So, bodies are moving on the ground. Best example, luggage bag. So, with a wheels, okay, you're carrying the luggage bag with wheels, right? So, the bodies are moving, right? Yes or no? So, with wheels. So, then it is comes under rolling friction. If the body is moving like a bus, car, cycle, okay, so they are moving on the ground, right? So, they are rolling on the ground, right? Then friction will be less. So, when the bodies are at rest position, friction will be more. When the bodies are at rest position, friction will be more. That is called static friction. What is that friction?

[00:40:52]Static friction. Okay, so static friction is greater than the sliding friction and rolling friction. Because when the bodies are sliding or each other uh one body is sliding over another, so there is interlocking of irregularities. Okay, so interlocking of irregularities will be less. So, there is no time for interlocking of the surfaces. Then friction will be less.

[00:41:18]Compared to the static friction, in sliding friction, friction will be less.

[00:41:23]Compared to the uh rolling friction, compared to rolling friction, sliding friction is greater.

[00:41:31]Compared to sliding and rolling, static friction is greater. So, which one is greater? Static friction. After the that, second position, sliding friction. After that, rolling friction.

[00:41:46]So, here you have to observe the interlocking of irregularities. Okay, so at the static friction, the bodies are at rest position, interlocking will be more. Sliding, so time will be less.

[00:42:00]Less time to contact. Less time to interlock interlock. Whereas rolling friction, so no time for it. So, keep on moving, right?

[00:42:09]Then friction will be less.

[00:42:12]Right? So, this is about uh static friction, sliding friction, rolling friction.

[00:42:20]Understood or not? So, now I'll draw the graph.

[00:42:26]I'll draw the graph.

[00:42:30]Okay? So, let's discuss about it.

[00:42:47]I'll draw the graph, so let's discuss about it.

[00:42:57]So, friction So, here applied force.

[00:43:16]So, then the FS equal to μs into R.

[00:43:30]FK equal to μk into R.

[00:43:34]So, the body is start sliding.

[00:43:39]Okay? The body start moving.

[00:43:43]All right? So, this here kinetic friction kinetic friction So, max value of static friction limiting friction here.

[00:44:02]Limiting friction The max value of static friction.

[00:44:08]Value of static friction.

[00:44:16]Maximum value of static friction.

[00:44:20]Understood or not?

[00:44:22]Is it clear?

[00:44:24]So next one static friction.

[00:44:34]Static friction. So this is the graph.

[00:44:38]This is the graph. Understood or not?

[00:44:40]So observe carefully.

[00:44:42]So applied force friction.

[00:44:46]So static friction here this is static friction.

[00:44:49]Here maximum value of static friction.

[00:44:51]So when the body start moving when the body start moving kinetic friction will be there. Limiting friction fs equal to μs into r. fk equal to μk into r.

[00:45:04]Is it clear or not?

[00:45:06]Yes or no?

[00:45:08]Yes. So next So we will discuss about We will discuss about Kinetic friction completed.

[00:45:46]Now we'll discuss about connected bodies.

[00:45:51]Okay. So placed adjacent side.

[00:45:54]Then we will see here.

[00:45:56]So I'm taking like this.

[00:46:00]One two So, force is acting here.

[00:46:08]m1 m2 acceleration A So, force is acting on it m1 m2. So, acceleration will be in this direction.

[00:46:20]Understood or not? So, now you can see F = MA.

[00:46:27]F = MA nothing but m1 + m2 into A.

[00:46:33]So, A = F by m1 + m2. So, equation one.

[00:46:41]Yes or no? F = MA F = MA So, F = m1 + m2 into A.

[00:46:52]So, then A = F by m1 + m2.

[00:46:56]That is equation one.

[00:46:58]Is it clear or not?

[00:46:59]Yes. So, now contact force on m1 contact force on m1 that is So, you can see here So, contact force on m2 Okay, so I hope it is very clear.

[00:47:39]Understood or not?

[00:47:41]So, just check once.

[00:47:47]So, m1 m2 acceleration force is acting on it. F = MA So, F = m1 + m2 into A. A = F by M1 + M2. Equation 1 M1A M1F by M1 + M2 equation.

[00:48:04]So, So, from this equation two we can take equation two equation three Understood or not? So, next Next, we will discuss about So, now I connected two bodies. So, next time I'll connect three bodies.

[00:48:26]Right? Shall we connect?

[00:48:32]Attached.

[00:48:35]Three bodies are attached. What happens?

[00:48:38]We'll see.

[00:48:56]One two three M1 M2 M3 force acting on it.

[00:49:08]F acceleration will be there. Yeah.

[00:49:14]Okay?

[00:49:15]So, now you have F = MA.

[00:49:18]Yes or no?

[00:49:20]Newton's second law.

[00:49:31]M1 + M2 + M3 into A. So, A = F by M1 + M2 + M3 equation one equation one Understood or not? Understood or not?

[00:49:54]now we can see So, contact force between M1 M1 here M2 M1 M F2 F2 Okay, contact force between M1 and M2 is F1. Contact force between M2 and F3 is F2.

[00:50:16]Right? So, now we can see uh contact force F1 equal to M2 + M3 into F by M1 + M2 + M3 So, equation two.

[00:50:38]Contact force between M2 and M3, that is F2.

[00:50:42]F2 equal to M3 F by M1 + M2 + M3 So, equation three.

[00:50:57]Is it clear or not? Just check once.

[00:51:08]Is it clear?

[00:51:59]>> So, next one.

[00:53:54]>> So R equal to mg cos theta equation one Okay?

[00:54:04]R equal to R equal to mg cos theta. So because So there is no movement along the vertical direction.

[00:54:18]Only horizontal direction only movement is there, right? There is no movement in the vertical direction, that's why R equal to mg cos theta. Is it clear?

[00:54:28]Now you can see so body is moving downward direction.

[00:54:33]So FS equal to mu s into R So FS equal to mu s into mg cos theta mg cos theta. Understood or not?

[00:54:54]Now mg sin theta minus mu s into mu s into mg cos theta mu s into mg cos theta equal to ma So this is the m.

[00:55:18]Okay?

[00:55:19]Now So here you can take m g are taking common.

[00:55:26]sin theta minus mu s into cos theta equal to ma. So mm get cancelled.

[00:55:34]a equal to g into sin theta minus mu s into cos theta.

[00:55:43]So, equation one.

[00:55:46]Equation two.

[00:55:49]Understood or not? So, like this we can do it.

[00:55:56]Is it clear or not?

[00:55:58]Just check once.

[00:56:01]So, next Okay, so like this we can take.

[00:57:19]Okay.

[00:57:20]So, now you have equal to T1.

[00:57:24]The acceleration will be here because applied force is there along this direction.

[00:57:32]F equal to T1. Now, if you want to find out T2 T2 equal to M2 plus M3 into So, actually F equal to MA right.

[00:57:47]So, M equal to M1 plus M2 plus M3 into A.

[00:57:55]A equal to F by M1 plus M2 plus M3.

[00:58:03]Understood or not? So, this is equation one.

[00:58:08]Equation one.

[00:58:11]Now, you can see here. So, F So, we can find out A. So, T2 equal to So, here we have to we are finding T2.

[00:58:21]T2 equal to M2 plus M3 into A.

[00:58:25]Acceleration.

[00:58:27]So, now M2 plus M3 into Acceleration is nothing but F by M1 plus M2 plus M3.

[00:58:39]So, equation two.

[00:58:42]Equation two.

[00:58:45]Understood or not? So, coming to the T3 T3 equal to M3 F by M1 plus M2 plus M3. So, equation three.

[00:59:01]Understood or not? So, just check once.

[00:59:07]Okay, so is it clear?

[00:59:10]Check once.

[00:59:21]Is it clear or not? Just check once.

[00:59:42]>> So next So after connected bodies, so we'll do the pulley mass system.

[01:00:19]pulley mass system Okay, so observe carefully here.

[01:01:07]This is the diagram.

[01:01:09]This is the diagram. M1G acting downward direction.

[01:01:13]So acceleration is downward, so because So here condition is M1 is greater than M2.

[01:01:22]Condition is m1 is greater than m2. m1 is greater than m2.

[01:01:28]Right? So, now we can take m1g - t = m1a.

[01:01:36]Equation one.

[01:01:39]So, t - m2g = m2a.

[01:01:46]Understood or not?

[01:01:48]m1g - t = m1a.

[01:01:52]So, t is greater because body is moving upward direction.

[01:01:56]m2 is moving upward direction. So, that's why t - m2g = m2a. So, if you add these two equations equation two, if you add one and two one and two, you'll get So, here you can see Now, m1g - t + t = m2g = m1a + m2a.

[01:02:49]So, this will get cancelled.

[01:02:52]Then m1g - m2g = a you're taking common m1 + m2.

[01:03:01]So, a = * g / m1 + m2.

[01:03:12]So, equation three.

[01:03:16]Understood or not?

[01:03:18]So, very simple.

[01:03:20]So, we have to write the equations.

[01:03:23]That's enough.

[01:03:24]If you know how to write the equation, so these problems are very, very easy.

[01:03:30]We can do it in easy way.

[01:03:33]Okay, so this is a pulley mass system.

[01:03:38]Understood or not?

[01:03:40]So, next one.

[01:03:42]So, one more one more condition, one more case.

[01:04:40]Okay, in this case, one subject.

[01:04:43]Now, you can see a So, again, m1 is greater than m2.

[01:04:52]Again, m1 is greater than m2 condition.

[01:04:59]So, m1 is greater than m2.

[01:05:05]So, we can write the equations.

[01:05:09]So, that is So, m1g is greater, so m1g minus t equal to m1a, equation one.

[01:05:21]So, here tension t equal to m2a, equation two.

[01:05:27]Say add one and two.

[01:05:30]Then you'll get the m1.

[01:05:32]Okay, in the place of Uh even if you add also, you'll get same thing.

[01:05:39]m1g minus t plus t equal to m1a plus m2a.

[01:05:47]Even if you substitute or even uh you do yourself, you'll get same.

[01:05:52]So, a equal to m1g by Equation three.

[01:06:05]Equation three.

[01:06:07]So, same a you can substitute here.

[01:06:10]Tension equal to m1 m2 Okay, g equal by m1 plus m2.

[01:06:24]So, tension you can substitute. So, here is the tension. Tension you can here. t equal to So, from equation two I'm taking.

[01:06:34]From equation two.

[01:06:38]Equation two. So, t equal to uh in the place of a, okay, say how to substitute m1g. m1g into m2 by m1 plus m2.

[01:06:51]m1 plus m2. Understood or not?

[01:06:53]So, just check once. So, very simple equation.

[01:06:57]Very easy equation. If you like the content, if you like the channel, do like, share, and subscribe to Student the Brain.

[01:07:04]Do like, share, and subscribe to Student the Brain.

[01:07:08]Very simple.

[01:07:10]And one more equation one more case I'll be taking.

[01:07:15]One more condition, one more case.

[01:07:19]So, here same diagram same diagram, no change.

[01:07:33]Same diagram, not changing.

[01:07:36]But a small modification. Same diagram.

[01:07:40]Everything will be same, but a a small modification.

[01:07:44]Okay, so that is fric- surface is friction surface.

[01:07:51]So, weight is acting M2 is acting downward direction.

[01:07:55]Reaction force is acting.

[01:07:57]So, mu s into M2G.

[01:08:02]That's enough.

[01:08:04]Now again, how the equation will be changing. So, now you can see again M2 is greater than M1 Sorry, M1 is greater than M1 is greater than M2.

[01:08:17]So, here same. How to write the equations?

[01:08:21]See here, M1 M1G minus T equal to M1A equation one.

[01:08:29]So, here tension T tension is there and friction also there, right?

[01:08:34]Tension is there as well as friction also there. So, that's why mu s into M2G equal to M2A. So, equation two.

[01:08:45]So yes add two equations. If you add M1G minus T plus T minus mu s into M2G equal to M1 plus M2 into A. Directly I'm writing Anyway, t t get cancelled.

[01:09:08]So, g I'm taking common.

[01:09:11]m1 minus mu into m2 equal to m1 plus m2 into a.

[01:09:20]Then a equal to So, m1 minus mu s into m2 into g by m1 plus m2. So, equation three.

[01:09:34]So, acceleration you got it, right?

[01:09:36]You got the acceleration.

[01:09:39]So, now you can substitute here.

[01:09:41]If you substitute, you'll get the remaining equation.

[01:09:45]Okay? So, very simple.

[01:09:47]If you substitute the acceleration in equation two or acceleration in equation one also, any one equation if you substitute, you'll get it.

[01:10:01]Right?

[01:10:03]Yes.

[01:10:06]So, one more example.

[01:10:10]One more example we'll take.

[01:11:14]>> Okay.

[01:11:15]So, check this one.

[01:11:19]Now, try to write the equations.

[01:11:23]Try to write the equation.

[01:11:25]So, condition is M1 is greater.

[01:11:30]Okay.

[01:11:32]So, observe the acceleration in which direction acceleration is there.

[01:11:37]So, accordingly you can write the equation.

[01:11:41]Okay. So, if you like the content, do like, share, and subscribe to Student the Brand.

[01:11:46]So, this is Vasu sir.

[01:11:49]Now, you can see here.

[01:11:57]M1 g - T1 equal to M1 a equation one.

[01:12:04]Here, T1 - T2 equal to capital A.

[01:12:10]Equation two. Coming to the M2.

[01:12:13]T2 - M2 g equal to M2 a.

[01:12:18]Equation three.

[01:12:21]Okay. Add all these three equation one, two, and the three.

[01:12:27]M1 g - T1 + T1 T2 + T2 M2 g equal to a I'm taking common M1 + M2 into capital M.

[01:12:44]Okay.

[01:12:46]So, here you can observe T1 T1 get cancelled. T2, T2 get cancelled.

[01:12:55]Then remaining values are G I'm taking M1 minus M2 equal to A into M1 plus M2 plus capital M.

[01:13:09]So I want A value, so A equal to M1 minus M2 into G by M1 plus M2 plus capital M.

[01:13:22]So this the acceleration, so equation four.

[01:13:26]So you can substitute acceleration in any of three equations.

[01:13:32]So substitute acceleration so any of the equations three.

[01:13:39]So any one equation, you'll get tension, so next T2 like that.

[01:13:45]So if you're substituting uh uh first equation, you'll get T1. If you're substituting uh equation three, you'll get T2.

[01:13:54]Okay, so likewise, you can substitute and get the values.

[01:13:59]So is it clear or not?

[01:14:02]Okay, done. So coming to the next one.

[01:14:30]So one more equation, so here you can see turn turn turn turn turn inclined wedge.

[01:14:56]m1 m1 g acceleration here t t m2 So, yeah.

[01:15:10]Weight is acting m2 g m2 g cos theta theta and here m2 g sin theta and we normal reaction r Okay?

[01:15:26]So, now you can see here.

[01:15:32]So, how to write the equation?

[01:15:39]m1 g minus t equal to m1 a equation one So, tension so object is moving upward direction because so m1 is greater than m2 Now, t minus m2 g sin theta equal to m2 a equation two Okay, so add one and two.

[01:16:12]If you add one and two, then you'll get 1 + 2 So, m1 g minus t plus t minus m2 g sin theta m1 plus m2 into a So, here we can cancel t t.

[01:16:37]Then g you are taking common.

[01:16:40]m1 minus m2 sin theta = m1 + m2 into a Then a = m1 - m2 sin theta into g by m1 + m2 equation three Is it correct or not? Just check once.

[01:17:12]Either see the equations.

[01:17:16]See the equations.

[01:17:22]Is it clear or not?

[01:17:26]Okay.

[01:17:28]So I hope it is very clear.

[01:17:33]So coming to the next one, anyway acceleration you got.

[01:17:37]Now if you substitute in equation one So acceleration if you substitute in equation one you will get tension.

[01:17:44]Okay. So if you like the content, if you like the channel, do like, share and subscribe to Student Ebrand.

[01:18:07]So one more m1 m1 g cos theta m1 g sin theta reaction force tension your tension So m2 So m2 g m2 g cos theta m2 g sin theta reaction force of Okay?

[01:19:09]So in this case how to do it?

[01:19:12]So as same m1 is greater than m2 So we have to consider acceleration for that purpose I'm taking We can take reverse also.

[01:19:27]Now I'm taking m1 is greater then you can take m2 is greater then write the equation.

[01:19:33]Okay? So you'll get a practice.

[01:19:36]Okay? So try to practice that.

[01:19:40]So very simple only very easy just see here m1 is greater than tension because body is moving downward direction towards that uh force gravity component is m1 g m1 g sin theta minus t equal to m1 a equation one And here t minus m2 g sin theta equal to m2 a So equation two So add equation one and two Add equation one and two then you'll get m1 g sin theta minus t plus t equal to m2 g sin theta equal to m1 plus m2 into a.

[01:20:34]So, here you can see So, tension tension get cancelled. Okay?

[01:20:40]So, because same only.

[01:20:42]Now, g I'm taking common.

[01:20:45]m1g sin theta and the sin theta also we can take common, right?

[01:20:52]Oh, yeah.

[01:20:56]So, we can also take theta one theta two also we can take.

[01:21:01]So, then it varies.

[01:21:06]So, here theta one and here theta two.

[01:21:10]Theta two cos theta two theta one cos theta one like this.

[01:21:18]And here first equation is sin theta one sin theta sin theta two second equation.

[01:21:26]Sin theta one sin theta two and here sin theta one sin theta two. So, two different angles you can take.

[01:21:34]Different angles. Okay?

[01:21:36]So, here I m g one m one g sin theta one m one g cos theta one because theta one here theta one here theta two m one m two g cos theta two m two g sin theta two theta two.

[01:21:51]Okay, done. So, m one g So, first equation m one g sin theta one So, m two g sin theta two. Okay, so okay okay okay okay.

[01:22:01]Okay, done. So, a equal to m one plus m two.

[01:22:07]Now, so a equal to m one sin theta one minus m two sin theta two into g by m one plus m two.

[01:22:25]Okay?

[01:22:27]Okay.

[01:22:29]the equation three.

[01:22:32]Is it clear?

[01:22:36]So, like that we can do it. If you like the content, if you like the channel, do like, share, and subscribe to Student the Brand.

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