Hey guys. So in this video, we're going to talk about how different kinds of motion give you different kinds of energy. And I'm going to walk you through a comprehensive list of all the possibilities you might see so that for any kind of problem, you always know what kind of energy goes with the problem, what kind of energy exists in that situation? Let's check it out. So what we want to do here is make sure that we know which energies go with a particular situation. A particular situation. Now, a potential problem arises when you have point masses. And that's because point masses, if you remember, if they're going a circular path, they have rotational speed. So if you have a tiny little mass here,
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Types of Motion & Energy: Study with Video Lessons, Practice Problems & Examples
Different types of motion correspond to specific forms of energy. For instance, a box moving in a straight line possesses only linear kinetic energy, while a spinning disk has rotational kinetic energy. When analyzing a point mass in circular motion, both linear velocity (v) and angular speed (ω) can be used to calculate kinetic energy, but they represent the same motion. The total kinetic energy (Ktotal) is calculated using either KL or KR, ensuring not to double count. The equations are: 1/2mv^2 and 1/2Iω^2.
Types of Motion & Energy
Video transcript
Kinetic Energy of a Point Mass
Video transcript
Hey guys, in this video, I'm going to show you how there are 2 ways to calculate the kinetic energy of a point mass going around a circle. Let's check it out. Alright. So remember, if you have a point mass around a circle, under a circular path, it's kind of like this, around a distance of little r from the axis of rotation. You have rotational speed, omega. And you also have a linear equivalent, which is your tangential velocity. Okay? All right. But you only have one type of motion. All you're doing is this. Okay? Your only motion is really rotational motion. Your only motion is rotational motion, so you only have one type of kinetic energy. Okay. But you can calculate using KL or KR. You can use the equation for linear or for KR. And that's because these two equations, as I'm going to show you now, are equivalent. Okay. The most important thing to do here is to make sure you don't double count it, okay? When I ask you for the total kinetic energy of an object, you can't, point mass like this. You can't look at it and say, well, it's got a V, so it has a linear kinetic energy and it has an omega, so it has a rotational kinetic energy. It's got 2 kinds of energies. Let's add the two of them together. You can't do that because these guys are equivalent, right? The tangential velocity is basically a mirror of omega. It doesn't mean there's 2. It just means that, one basically reflects the other, all right? So what you can't do is double count. So let me show you how this works. A small 2-kilogram object, so mass equals 2 kilograms, is going around, with a rate of it's going around the vertical axis. So what is a vertical axis? Remember axis, you can think of it as an imaginary line that you spin around. So a vertical axis would look like this. So it means the object is going around like this. Okay? Like this. Cool. So they would actually I could draw it like this and the object is doing this. Okay. And it does this at a rate of 3 radians per second, maintaining a constant distance of 4 meters to the axis. This distance to the axis is what we call little r. Little r is 4 meters. And I want to know the object's kinetic energy, and I want to do this using the KL equation, the KR equation. And the purpose of this question is to show you how the answer ends up being the same, and I'm going to summarize it at the end. So we can do KL, we can do KL, which is going to be half MV2. Okay. Remember that these 2, V and r, are related, right? V and r are related by V equals romega. So what I'm going to do is also write KR equals half I omega. And I'm going to rewrite one of these equations one of these equations, and you're going to notice how it's going to look exactly like the other. So let's rewrite this one here. 1 2 I ω 2 remember, I for a point mass is MR2. So I'm going to replace this with MR2. And I can rewrite omega as well. V equals romega, so omega equals V over r. So instead of omega here, I'm going to put V over r. Now look what happens. This r squared cancels with this r squared, and we're left with half MV2, which is exactly this equation. Okay? So you can go from one to the other for a point mass, You can do this, which means I could have calculated them either way. Alright? So if I go here, KL equals half MV2. Let's get these numbers, omega equals 3, V equals romega, so omega equals V over r, V, I'm sorry. I'm trying to get V. So V equals r4omega3V is 12, so this is half mass is 2. They cancel 12 squared. So this is 144 joules. Cool? And if I wanted to do it using KR, I already showed you how the equations turn out to be the same. Now I'm just going to plug in numbers differently. So if I wanted to do it this way, I could have done 1 2 M R 2 ω 2 half, right, which is this. Half the mass is 2, and the distance is 4 squared, and the omega is 3 squared. So these 2 cancel. I have 16 times 9, which is 144 joules. Okay. So if you calculate it using linear, it's 144. If you calculate using rotation, it's 144. And if I ask you what is K total, the answer is 144. Okay. And I want you to please write here not 288. You do not add the 2. You can get the same answer using the two different equations. Now, to make this simpler for you, I have a convention. I always think of an object going around a circle like this. It has one motion. I always think of this as linear motion. I always I'm sorry, rotational motion, not linear. So I would always do it like this, KL plus KR, and I would say there's no KL, there's only KR, and this will guarantee that you don't double count it. Cool? So this is just a potentially tricky thing, but once you understand it, get it out of the way, it's never going to bother you again. Cool? Let me know if you have any questions.
The Earth has mass 5.97 × 1024 kg, radius 6.37 × 106 m. The Earth-Sun distance is 1.5 × 1011 m. Calculate the Earth's kinetic energy as it spins around itself. BONUS:Find the Earth's kinetic energy as it goes around the Sun.
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More setsHere’s what students ask on this topic:
What is the difference between linear kinetic energy and rotational kinetic energy?
Linear kinetic energy is the energy an object possesses due to its motion in a straight line. It is given by the equation
How do you calculate the kinetic energy of a point mass in circular motion?
To calculate the kinetic energy of a point mass in circular motion, you can use either the linear kinetic energy formula
Can an object have both linear and rotational kinetic energy simultaneously?
Yes, an object can have both linear and rotational kinetic energy simultaneously. This occurs in cases of rolling motion, where an object not only spins around its own axis but also moves linearly. For example, a rolling wheel has both linear kinetic energy
Why can't you double count kinetic energy in circular motion?
You can't double count kinetic energy in circular motion because the linear velocity v and angular velocity ω represent the same motion. Using both
What is the kinetic energy of the Earth as it orbits the Sun?
The kinetic energy of the Earth as it orbits the Sun is considered rotational kinetic energy. This is because the Earth's center of mass moves in a circular path around the Sun. The kinetic energy can be calculated using the rotational kinetic energy formula