Under Circular Motion

[00:00:04]Hello. Special greetings to all of you and welcome to Acadeex Committee, the Citadel of Excellence.

[00:00:17]I am Sir Godwill Jakum and in today's class, I'll be taking you through a physics class.

[00:00:31]And we're going to be discussing circular motion.

[00:00:39]We're going to be discussing simpler motion. So you give me a minute. I'll push the the link to your friends so that they're going to join me and then we're going to work together.

[00:01:23]Okay, perfect.

[00:01:37]Yes. So we are starting we're going to be discussing circular motion and we're going to start from the base. It means even for those of you who have you have never done circular motion before no worries because I'm going to be explaining everything and um I'm going to explain detail not just that we're going to cover the entire topic of secular motion.

[00:02:22]So therefore, I am inviting you to exhaust a lesson like this one in a in a calm environment, in a very calm environment. And you you if you are in a noisy environment, you can use headsets, you can use airports, you can use maybe an UF so that you concentrate. Also I recommend that you should of course have a notepad somewhere. You cannot be watching me like the way you watch Nigerian films or Indian movies. You should be active when you are watching.

[00:03:00]We should be working together.

[00:03:02]So we are talking about secular motion.

[00:03:04]I'll start by giving you the objective of the lesson.

[00:03:09]So the objectives as follows. At the end of this lesson, learners should be able to who are the learners? So, by the end of this lesson, you should be able to define circular motion. Distinguish between the types of circular motion.

[00:03:26]You already know that there are two type of circular motion. We'll talk about them.

[00:03:32]Next, define angular displacement, angular velocity, and angular acceleration.

[00:03:38]Next, explain the meaning of radian.

[00:03:41]Next, establish the relationship between angular velocity, frequency, and period.

[00:03:49]Next, [snorts] establish the relationship between linear velocity and angular velocity.

[00:03:55]Next, explain centripal acceleration.

[00:04:00]Next, derive the expression for centripal acceleration. Next, derive and apply the expression for centripal force.

[00:04:10]Next, explain circular motion on horizontal and banked root.

[00:04:17]Next, analyze vertical motion.

[00:04:22]Vertical circular motion.

[00:04:25]Explain that's next. Explain the motion of satellites in circular orbit. Solve numerical problems.

[00:04:35]to solve numerical problems involving circular motion. So that's a that's a that's a program.

[00:04:43]Yes, a rundown. That's what we're going to be doing. So you see it's long. So I'm going to be very sharp. I'll explain detail. It doesn't mean that I'll not be fast. So I'll be super fast and I want you to concentrate and um you can you can be in the comment if you have any question you can let me know in the comment section so that I would um I'll be immediately notified on my phone which I have with me then I can answer to your question directly since I I am lying. So what is circular motion?

[00:05:30]From the word circular motion, it simply means in simple pralance that what circular motion means motion in a circular path and that's self-sufficient.

[00:05:41]Um what you need to know about circular motion is that it is a kind of motion in which the particle undergoing motion is moving in the path of a circle or is moving in a circular path. So the motion of an object in the circular path about a fixed point and that fixed point is known as the center. Now what are certain examples of circular motion?

[00:06:08]Some examples of circular motion may include the mo the motion of the hand of the clock. I'm not going to draw the clock the the clockwise direction movement of the hands of the clock portrays circular motion. The ceiling fan if the camera could show up you will see it when it's turning it is taking the path of a circle. That's cular motion. The tire the the wheel of the car when the when the when the car tire is turning in motion it portrays what? Circular motion.

[00:06:50]Uh the moon the moon moves around the sun right and it is a satellite.

[00:06:58]Um the earth is a planet. It moves around the sun.

[00:07:03]Yes. Okay. the the the earth moves around the sun and then the the moon revolves around the earth because the and the earth has its own satellites.

[00:07:19]All of them that are moving around like that, it's circular motion.

[00:07:24]And um satellites that are moving around the head, I've mentioned them. Then um what again?

[00:07:33]If you tie if you tie a a stone on a on a rope and you begin to swing it in the form of a circle, it under go circular motion. So now what are the types of circular motion? There are two of a particle in path with what?

[00:08:01]Constant speed.

[00:08:07]With constant speed, the speed is not changing. In uniform circular motion, the speed remains the same.

[00:08:16]When the speed remains the same, when the speed remains the same, it is clear that acceleration is zero. When the when the speed remain the same, it means that the particle is not accelerating and therefore the centripal acceleration AC is equal to zero. We'll come to that.

[00:08:39]Now, why didn't I talk about constant velocity here?

[00:08:43]constant in uniform circular motion even though the speed is constant. Why?

[00:08:49]Because of the notion of the direction.

[00:08:54]Now look at me look at the body here.

[00:08:57]When the body is undergoing circular motion, the body is portraying a path like this.

[00:09:03]This is the center here. The the the path is in the form of circle.

[00:09:10]Now look here.

[00:09:15]In which direction is the particle moving?

[00:09:19]When it is turning the form of a circle, the direction keeps changing.

[00:09:25]The direction keeps changing. Imagine you tie a stone on a rope and you swing it. When you are doing this, if the rope cuts, does the stone continue moving in the circle? No. It will follow the direction at that point. So if the rope cuts here, the stone will go like that. If the rope cut here, the stone will go like this.

[00:09:54]If the rope cut here, the stone will go like this. So you see that in the c in circular motion, the direction keeps on changing. And what is the difference between speed and velocity? The difference is simple and clear.

[00:10:10]Speed is what? A scalar quantity velocity is a vector quantity. Meaning velocity takes into cons concentration the direction. Since the direction keeps changing means that the velocity keeps changing. On the other hand, nonuniform circular motion. Okay, let's first give some examples of uniform circular motion. motion of a particle in a circular path but the speed does not change. The hand of the clock is a good example as that clock is turning there's no day that it will turn faster or slower.

[00:10:47]Okay. So it is uniform uniform circular motion.

[00:10:52]Then another example is you can send your comments in the comment section.

[00:10:57]I'll I'll read them. Another example is the the the ceiling fan.

[00:11:05]It portrays what? Uniform circular motion. What again? The motion of satellites.

[00:11:12]Uniform circular motion. Now non-uniform circular motion. I said the speed changes. And some examples is a car taking a bend.

[00:11:23]When a car is taking a bend, it is portraying circular motion. But if the car is taking a bend and then it's accelerating, it means that it is no longer uniform circular motion. It's nonuniform circular motion. Even if the car is taking a bend and then reduce the speed, it is already nonuniform circular motion. And that is what happens in most in most cases at the level of a car taking a bend.

[00:11:53]So after discussing that now um we are going to continue with angular displacement.

[00:12:03]Yes. Um yeah I can see some people commenting.

[00:12:10]Yeah you can first of all start by commenting your name and where are watching me from. Yes, you can comment your name and tell me where you're watching me from.

[00:12:25]Now we are going to the angular displacement.

[00:12:33]Angular displacement when a particle is moving in in a circular path it displacement it has a certain angular displacement which is the angle the angle to which the motion of the particle is being uh the angle to which The motion the direction of motion of the particle that's the direction the the angle of the direction is what the angular displacement. So it is measured since an angle is measured in theta in degrees.

[00:13:16]It is recorded as data measured in degrees or in rats where it is important to know that one degree can be converted to rats and radians can equally be converted to what? converted to degree. How? Using pi. Pi is 90°.

[00:13:57]Meaning that what?

[00:13:59]2 pi is 360°.

[00:14:03]So you can now be able to convert from pi. Right. Pi is in radians.

[00:14:10]Pi when we usually call pi 22 and 7 or 3.14 it is in radians.

[00:14:22]Are we together? Now you can convert you can convert from radians to to degrees and vice versa.

[00:14:33]So it means that the SI unit for angular displacement is what is the radian and then um anyway we're going we're going to come we're going to come back to it again but for now I've already shown you how to convert from degree to radians is okay now we are going to look at angular velocity after we have already discussed angular displacement right angular disment is theta. Now let's talk about angular velocity. You know velocity is what?

[00:15:08]Displacement on time.

[00:15:10]Right? Velocity is what? Displacement on time. So angular displace angular velocity. Now angular velocity is denoted is represented by the symbol omega.

[00:15:33]And it is displacement angular displacement on time. So it means that omega is what [clears throat] data on t.

[00:15:45]Yes, we're going to we're going to first leave it at that level. Yes, we're going to first of all leave omega here. But we I'm going to as we continue I'll derive more [clears throat] ways through which you can calculate the angular velocity omega. Then now listen listen very well.

[00:16:08]What does it mean? Theta the SI unit for angular displacement is and the SI unit for time for time is second. It means that the SI unit for angular velocity omega is what? That per second, right? Okay. Now, very good.

[00:16:33]That's very good.

[00:16:36]That's nice that you're understanding.

[00:16:39]So, now uh we'll just move on. I'll talk to you on what frequency and time. What is frequency?

[00:16:48]Frequency will be short. So I'm not going to spend much time talking about frequency. Frequency is the number of revolutions.

[00:16:58]The number of revolutions on per time time taken. So it means that frequency is what? Number of revolutions on time.

[00:17:11]Are we together? So, how many times did a particle go around and how long did it take for the particles to finish going around? That's frequency.

[00:17:25]And the frequency is measured in what?

[00:17:28]Per second or hertz. And SI unit is hertz.

[00:17:39]Okay. Then from there now we can directly talk about period t. Period is the time for one oscillation meaning that the time for the particle to go around once is the period. Okay.

[00:17:59]And period is one over frequency meaning that what frequency is what? One over period. And the period is measured in second while frequency is measured in per second.

[00:18:14]Then we continue.

[00:18:22]All right.

[00:18:30]Now, we're going to use this. We're going to use this now. And then I will still talk to you back on the angular velocity omega where we said is the same as theta on data on c right.

[00:18:47]Good.

[00:18:50]Now omega is equal to theta on c.

[00:18:58]What is theta?

[00:19:00]Theta is the angular displacement.

[00:19:04]Okay. Angular displacement to go around like this.

[00:19:11]The angular displacement theta is what? 2 pi. I hope I explained that to you already.

[00:19:19]Theta is what? 2 pi.

[00:19:23]We leave that there. T the time for one oscillation is period t.

[00:19:32]Okay. So what are we saying?

[00:19:36]Uh sorry this is not theta now it's omega right? Yes because theta is 2 pi.

[00:19:42]So omega is what? Theta on t. Omega is 2 pi on t. Are we okay? So for one osation omega is what? 2 pi on t. That's that's formula and then we are just saying that 1 / t is is f frequency. It means that what omega is equal to 2 pi f a very beautiful formula that you should not forget.

[00:20:08]So [clears throat] I'm not I'm not going to be saying this and giving you examples for you to solve this and that for now. I'll first explain the the concept then questions.

[00:20:21]Okay.

[00:20:23]I hope it's clear. Now we are going to continue.

[00:20:33]Yes, we now proceed to look at the linear velocity the relationship between the linear velocity V and the angular velocity omega. Okay.

[00:20:59]Okay.

[00:21:08]Yeah. So, we'll we'll get down on that now.

[00:21:20]Now it's simple.

[00:21:26]Linear velocity V is equal to R omega where R is what? The radius. The radius.

[00:21:33]And what is the radius? Look here.

[00:21:36]In a simple part like this one, the radius a distance from the center to anywhere on the circumference. And what omega is the angular the angular velocity, right? Then this is the linear velocity. What does it mean? We are relating the linear velocity to the angular velocity.

[00:21:56]Okay. So we are saying that V is equal to R omega. Other people they just say V is equal to omega R. It's not the same thing. It's the same thing. Okay. So V is equal to R O omega. Meaning that omega is what? V on R. Omega is V on R.

[00:22:14]Okay. It's short and simple and clear, right?

[00:22:19]All right. So now we are going to talk about the centripal acceleration and then from the centrial acceleration now of course we have to look at the centripal force. Those are the two main things that we have to we have to talk about.

[00:22:39]Yes.

[00:22:51]Okay, good.

[00:22:53]From V equal to omega R. Let's V here represent what?

[00:23:05]V here represents the linear velocity.

[00:23:10]Omega represent the angular velocity. So want to use want to use it to come out with a to come out with a force.

[00:23:31]So the centrial acceleration Yes. The centrial acceleration is represented by AC. the centrial the centriital acceleration okay not to derive it I'll just go straight to the point the centrial acceleration is given by what let's come let's come to the linear velocity I said linear velocity linear velocity v is equal to what r omega Omega R now is equal to Omega R.

[00:24:23]Acceleration now is equal to what? R O omega².

[00:24:30]Now AC we represent AC being what? The centriital acceleration. And from there now it gives us the opportunity to be able to find the centrifugal force F represented as FC. From Newton's second law we know that F is equal to what? M E. Yes, you know this. So this is this is it.

[00:25:02]Meaning that FC is equal to M * A.

[00:25:05][laughter] The centrial force is equal to the mass time the centrial acceleration. Meaning that what f the centrial force is what? m r omega². So this is one of the most important formulas in circular motion. The formula to find the centriital force. What is the centrial force? The centrial force is that force that keeps the particle moving in the circular path.

[00:25:34]So the centrial force always act towards the center. For example, this part a particle is moving in the circle like this. There's a force that's acting towards the center. Wherever the particle is, the particle is here. The force there's a force that's acting towards the center of that part. Is that force that's keeping the particle to be moving in that center? That force is known as what? The centripal force.

[00:26:02]Now this this is acceleration with respect to what the the the angular velocity. Now with respect to what the the linear velocity acceleration of what acceleration centrial acceleration is what v ^ 2 / r.

[00:26:20]So what does it mean? Since f= m it means that the centri force is what? m * the centri acceleration. Same thing. So the centrial force will be what? m v 2 on r here is yet the most common formula for the centripal force. This is the formula that is used most often to resolve problems. So you use this one when you have the linear linear velocity then you use this one when you have the angular velocity.

[00:26:52]Okay. So very soon not from now we are going to be closing with this part and then I'm going to now giving you um questions we take questions God willingly I don't know I may answer them with you before I give you some as assignment or exercises we submit I'll correct that's Okay. Now let us talk about the properties of the centripal force. Since we have just mentioned centriital force here. Number one, centrial force acts towards the center of the of the circular part. Then the centripal force changes.

[00:27:44]It changes continuously and then why is it changing? Because the direction of the velocity is changing, right? The velocity is changing. So the force is also a vector quantity. So when the direction is changing, it means that the force is also going to what? The force is also going to change. Are we together?

[00:28:06]Good.

[00:28:07]Now question.

[00:28:10]A wheel rotate at a frequency of 5 hertz. Calculate its angular velocity.

[00:28:18]Yes. Uh angular velocity omega. Right.

[00:28:22]They have said that the wheel rotate at a frequency of 5 Hz. 5 Hz. Right. So want to find the angular velocity. Now the angular velocity is omega. It's supposed to what? 2 pi f. But this one is so simple, right? 2 pi f. You just put five here. 2 2 that's 2 2 pi * 5 that's 10 pi pi is what 3.14 or 22 / 7 use your calculator the answer is the answer will come out just like that do that well you will have 31.4 now your answer should be in rad per second because the the the SI unit for omega is what rad per second so it should be 31.4 before that per second.

[00:29:14]All right. Now, we're going to continue with the next.

[00:29:18]I'll just read the question is for you.

[00:29:21]A point A point on a rim of a wheel of radius 0.40 40 m rotates with an angular velocity of 20 rad/s.

[00:29:34]Calculate a linear speed. That one is for you. A body of mass 2.0 kg moves in a circular path of radius 0.50 m with a speed of 4.0 m/s.

[00:29:47]Calculate the centrial acceleration and be the centrial force.

[00:29:53]Okay, now that's the end of that uh question.

[00:30:01]So you're going to do that and in our next class we are going to look at motion in a vertical and a horizontal circle. So that means we would end here for today.

[00:30:14]I would say thank you for taking the class and please don't miss the next class.

[00:30:20]Um if you're preparing for any exam at all if you're preparing for any exam any exam then the best place to prepare yourself is acadeex cognitive yes it's acadeex so you can always contact the organization who the number 6 + 237 620 22 256 84 and you will always have someone to respond to you to answer your questions to provide you with maybe anything you need. You maybe you want to take off classes, get a a pamphlet, maybe pass question answer for exam and and so on. You see messages are coming in. Okay, so see you in the next class. This is it.

[00:31:18]It was a nice session with Sir God will Yakum lecturing from acadeon.

[00:31:30]Bye.