원운동의 구심력 이해하기

### 구심력의 이해: 주요 개념 및 응용
* 🔄 구심력은 물체를 원형의 경로로 계속 움직이게 하는 힘으로, 항상 **원의 중심**을 향합니다.
* ⚖ 속도와 같은 방향으로 힘이 작용하면 **물체의 속도가 빨라지고**, 반대 방향으로 힘이 작용하면 **속도가 느려집니다.**
* 🔄 힘이 속도에 수직인 경우 물체는 **속도 변화 없이 회전**하며, 이것이 구심력의 본질입니다.
* 🧗 밧줄에 연결된 공을 휘두를 때 볼 수 있듯이 **밧줄의 장력은 구심력을 제공**할 수 있습니다.
* 🚗 도로에서 회전하는 자동차에서 정적 마찰은 필요한 구심력을 제공하며, 이 구심력은 **다음 공식을 사용하여 계산**할 수 있습니다: \( \mu_s \cdot mg = \frac{mv^2}{r} \).
* 🌍 중력은 태양을 공전하는 지구의 구심력 역할을 하여 **지구가 우주로 날아가는 것을 방지**합니다.
* 📈 질량이나 속도가 증가하면 필요한 구심력이 증가하고 반경이 증가하면 **\( F_c = \frac{mv^2}{r} \) 공식에 따라 구심력이 감소**합니다.
* 🔍 구심력에 대한 자세한 이해를 돕기 위해 제공된 링크와 동영상 재생 목록에서 **실제 적용 사례와 문제 해결 기법**을 확인할 수 있습니다.

구심력은 속도에 영향을 주지 않고 방향을 바꾸어 물체를 원형 경로로 움직이게 합니다.

In this video, we're going to talk about the centripetal force. But when you hear the word centripetal force, what do you think about? Now, before we talk about it, let's go over a few things. So, let's say if we have an object that is moving to the right, and a force is acting on the object in the same direction as the velocity vector. What's going to happen to the object? If the force and velocity vectors are in the same direction, the object's speed will increase. It's going to speed up. Now, what if the force vector is in the opposite direction to the velocity vector? In this case, the object is going to slow down. Now, let's say if we have an object moving to the right, but this time the force vector is going up. It's perpendicular to the velocity vector. What's going to happen? The object, it's not going to speed up or slow down. Instead, it's going to turn. And that's what a centripetal force does. It causes an object to turn in a circle.

now centripetal has the key word sentry or center secant. This is a center secant force, and so the force is always directed towards the center of the circle, and thus that is a centripetal force. It's any force that keeps an object moving in a circle. Now, the centripetal force is not a force by itself; in fact, it's caused by other forces. So, here's an example. Let's say if we have a person, and he has a ball attached to a rope, and he's swinging his ball in a circle. So, what force provides the centripetal force in this case? Anytime you have a force acting through a rope, what is that force called? This force is the tension force. So, in this particular situation, tension provides the centripetal force. It keeps the ball moving in a circle. Now, let me give you another situation. Let's say if you have a car, which I'm just gonna draw a box, but this is a car, and it's turning on a road. It's following the curvature

of a road and it's turning. The fact that it's turning, there's some force that is causing it to turn. Let's say if it's moving at constant speed and turning at the same time, so there is a centripetal force acting on this car because it's moving in a circular path. What centripetal force, or rather what other force, provides the centripetal force in this case? If you see a situation like this, static friction provides the centripetal force. So if you're dealing with a physics problem that has a car turning on a road like this, make sure you set static friction equal to a central force. Now the formula for static friction is mu s times the normal force. It's less than or equal to this quantity. And for the centripetal force, it's mv squared over r. The normal force on a flat surface is simply mg. So in this case, we could cancel m in the expression. So for a word problem that involves a car turning on a road, you have this expression: the coefficient

of static friction times the gravitational acceleration is equal to v squared over r, and I'm going to pull some links in which you can practice these problems in another video. Now, let's say this is the sun, and here we have the earth, and the earth is orbiting the sun. So, the earth is moving in a nearly circular path around the sun, which means that there's a force that's acting as a centripetal force in this case to keep the earth moving with uniform circular motion. What force provides the centripetal force in this case? The force that keeps the earth in orbit around the sun is the gravitational force. And so, gravity provides the centripetal force in this example. Without gravity, the earth will fly off in a tangent away from the sun, deep into outer space. But because we have these two forces that are perpendicular to each other, the earth instead turns in a circular path. And so, make sure you understand this. Anytime you have a force that's perpendicular to the velocity component, I mean the velocity vector.

the force doesn't speed up or slow down the object. It has no effect on the speed if it's perpendicular to the velocity of the object. The force can only change its direction. Now, let's focus on the equation that relates to the centripetal force acting on the object. It's mv squared over r. So, here's a question for you. If the mass of the object increases, what will happen to the centripetal force? Will it increase or decrease? Because the mass is in the numerator of the fraction, an increase in the mass will increase the centripetal force. The same is true for the velocity. If you increase the speed of the object, the centripetal force that's needed to keep the object moving in a circle must be increased as well. Otherwise, the object is going to fly out of the circle. So, the greater the speed, the more centripetal force that is needed to keep the object moving in a circle. Now, what about if we increase the radius of the circle? What's going to happen to the centripetal force that is needed to keep

the object moving in the circle. If you use a wider circle, the centripetal force that's needed to keep it in that circle will decrease because r is in the denominator of the fraction. And so, let's focus on questions like these. What effect will the following changes have on the centripetal force acting on an object? So, what's going to happen if we double the mass? We know the centripetal force will increase, but by what factor? Now, the way in which you can get the answer is as follows: everything that doesn't change, replace it with for one. Now, because the mass increased by the factor of two, replace m with two. v and r, we're going to replace it with one. So, we get a value of two. This tells us that the centripetal force will double if we double the mass. Now, let's move on to part b. So, what effect will it have on the centripetal force if the speed is increased by a factor of two? So, the mass and the radius doesn't change, so we're going to replace it with

a one, but the speed is doubled, so we're going to replace it with a 2. 2 squared is 4, and so this tells us that the centripetal force will increase by a factor of 4. Now what about part c? The radius is decreased by four, let's say decreased by a factor of so what should we do m and v doesn't change, so we're going to replace that with a 1. If the radius is decreased by a factor of 4, that means that it's 1/4 of its original value. So we have one divided by one-fourth, which is four. If you want to show your work with that, what you need to do is multiply the top and the bottom by four. Four times one-fourth is one, and so you get four. Now what about the last one, part d? What effects will tripling the mass, quadrupling the speed, and cutting the radius in half have on the centripetal force acting on the object? So all we got to do is plug in these

numbers, so we're going to triple the mass, replace it with a 3. The speed is quadrupled, so we're going to replace that with a 4. And the radius was cut in half, so let's replace r with one-half. So we have 4 squared, which is 16. 16 times 3 is 48, and 48 divided by a half is the same as 48 times 2. And so we get 96. So the centripetal force will increase by a factor of 96 in this case. And that's basically it for this video. So I want to give you a simple introduction into centripetal force. Now for those of you who want actual problems regarding this topic, check out the links in the description section because I'm going to post some links to other videos that have more problems on this topic and other videos that you might be interested in. And when you get a chance, check out my new physics video playlist because I have these topics listed in order. And if you like this video, don't forget to subscribe to this.

channel for more informational content. So, I do have other videos on calculus, algebra, trade, chemistry, and other hard classes that people have difficulties with in high school and college. So, if you need help with those courses, feel free to check out my channel, and you might find something that could help you. Thanks again for watching.

Physics - What Is a Centripetal Force?

This channel focuses on providing tutorial videos on organic chemistry, general chemistry, physics, algebra, trigonometry, precalculus, and calculus.

Disclaimer:  Some of the links associated with the videos in my channel may generate affiliate commissions on my behalf.  As an amazon associate, I earn from qualifying purchases that you may make through such affiliate links.


My Patreon Membership Program:  (Full Extended Videos + Worksheets)
https://www.patreon.com/MathScienceTutor


The Organic Chemistry Tutor

구심력은 물체가 항상 중심을 향해 원을 그리며 회전하게 하는 힘입니다.

구심력은 독립적인 힘이 아니라 밧줄의 장력과 같은 다른 힘에 의해 발생합니다.

예를 들어 공을 휘두르는 사람이나 곡선 도로에서 회전하는 자동차는 모두 구심력에 의존하여 원 운동을 유지합니다.

도로에서 회전하는 자동차는 정적 마찰에 의해 구심력을 경험합니다.

정적 마찰의 공식은 평평한 표면에서 정적 마찰 계수에 정상 힘을 곱한 값인 mg과 같습니다.

태양 주위를 도는 지구 궤도의 경우 중력이 구심력을 제공하여 지구를 원형 경로로 유지합니다.

물체에 작용하는 힘은 속도에 수직인 경우 속도에는 영향을 미치지 않고 방향만 변경합니다.

구심력은 mv 제곱/R이라는 방정식으로 주어지며, 질량이나 속도가 증가하면 물체가 원 안에서 계속 움직이는 데 필요한 구심력이 증가하게 됩니다.

반대로 원의 반지름을 늘리면 구심력은 감소합니다.

속도를 두 배로 늘리면 구심력이 4배 증가하고, 반경을 4배 줄이면 힘도 4배 증가합니다.

질량을 세 배로 늘리고 속도를 네 배로 늘리고 반경을 반으로 줄이면 구심력이 96배 증가합니다.

이 채널에서는 미적분, 대수학, 무역, 화학 및 기타 어려운 고등학교 및 대학교 과정에 대한 동영상을 제공합니다.

시청자는 이 채널에서 유용한 콘텐츠를 확인하시기 바랍니다.

크리에이터는 시청자의 성원에 감사를 표합니다.