Anderson Video - Inertial Frames of Reference

Professor Anderson
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>> Hello, class. Professor Anderson here. Let's talk about something called inertial frames of reference. When we had talked about moving from a stationary frame to a moving frame and observing some behavior, we always talked about inertial frames of reference. But what does that really mean? What does inertial mean? What this means is the following. An inertial frame is one that has constant velocity. Your inertial frame has to have constant velocity. If there is constant velocity, that, of course, means acceleration A is equal to zero in that frame. Okay? Whatever frame you are in, you cannot have any acceleration. So let's imagine the following scenario. Let's say you're standing in an elevator and you're standing on a scale. Okay, and you have a weight of 100 newtons, but the force of the scale, the normal force of the scale reads 110 newtons. Are you in an inertial frame? [inaudible], you had asked this question. What do you think? If my weight is 100 newtons, but the scale is reading 110 newtons, am I in an inertial frame? >> I would say no because if the weight is -- if the scale is different from the weight, it means you are accelerating. >> Okay. >> And in inertial frame acceleration is zero. >> You are not in an inertial frame, exactly what [inaudible] said, because you are accelerating. Let's just double check and make sure that works. We know that the sum of the forces in the Y direction is equal to the mass times acceleration in the Y direction. The only forces here acting on this person are, of course, MG down, the normal force from the scale going up. So sum of the forces becomes N for the scale, minus MG, that's equal to the mass times the acceleration, and now we have numbers, 110 newtons minus 100 newtons is equal to the mass times acceleration. That is, of course, 10, and so we get a positive number for A. It's certainly not equal to zero, and that means that no, we are not in an inertial frame. If this was an inertial frame, [inaudible] what would the scale reading have to be? >> It would have to read 100 newtons. >> It would have to read 100 newtons. Absolutely right. And that can happen when the elevator's at rest, or when the elevator is moving with constant velocity. If it's moving up with constant velocity, then your scale reading is exactly the same as your MG, and the acceleration of the elevator is zero. And so when you think about inertial frames, just think of this. Is that frame moving at constant velocity? Now let me ask you a follow-up question. [inaudible] are you in an inertial frame right now, sitting there in your chair in this room, are you in an inertial frame? >> I would say yes, because acceleration is still in negative G. >> Okay. Are you accelerating at a negative G? >> Yes. >> You don't look like you're accelerating at negative G. >> Well, it's still pulling you down [inaudible]. >> Okay, something's pulling you down? Is it the weight of the school? All the pressure? Is that the weight? Are you accelerating right now? No. MG down, but what's pushing back up on you? >> Normal force? >> Normal force, right. So what's your acceleration right now? >> Zero. >> Zero, so are you in an inertial frame? >> No. >> Yes. You are if your acceleration is zero, but if you were moving at constant velocity, then you are in an inertial frame. Now that's, in fact, only an approximation. You in your chair in this room, moving at constant velocity, is that really right? Are we really moving at constant velocity? Is our acceleration equal to zero? >> It depends like what you're considering like relative to what -- >> Okay. >> Exactly, so in terms of like being on earth that's spinning, or rotating, then we are -- are not in inertial frame? >> Okay. Exactly right. We're sitting on the earth. The earth is spinning. We are moving in a circle right now. If you are moving in a circle, you are accelerating. You have centripetal acceleration, which means that you are in a non-inertial frame. Now that acceleration is very small compared to G, and so to a good approximation, we can say we are inertial. We are in an inertial frame. But technically speaking, it's really a non-inertial frame, because we're moving in a circle. All right. Good. Any questions about this stuff? You guys feeling okay about it? All right. If that's not clear, come see me in my office hours. Cheers.
>> Hello, class. Professor Anderson here. Let's talk about something called inertial frames of reference. When we had talked about moving from a stationary frame to a moving frame and observing some behavior, we always talked about inertial frames of reference. But what does that really mean? What does inertial mean? What this means is the following. An inertial frame is one that has constant velocity. Your inertial frame has to have constant velocity. If there is constant velocity, that, of course, means acceleration A is equal to zero in that frame. Okay? Whatever frame you are in, you cannot have any acceleration. So let's imagine the following scenario. Let's say you're standing in an elevator and you're standing on a scale. Okay, and you have a weight of 100 newtons, but the force of the scale, the normal force of the scale reads 110 newtons. Are you in an inertial frame? [inaudible], you had asked this question. What do you think? If my weight is 100 newtons, but the scale is reading 110 newtons, am I in an inertial frame? >> I would say no because if the weight is -- if the scale is different from the weight, it means you are accelerating. >> Okay. >> And in inertial frame acceleration is zero. >> You are not in an inertial frame, exactly what [inaudible] said, because you are accelerating. Let's just double check and make sure that works. We know that the sum of the forces in the Y direction is equal to the mass times acceleration in the Y direction. The only forces here acting on this person are, of course, MG down, the normal force from the scale going up. So sum of the forces becomes N for the scale, minus MG, that's equal to the mass times the acceleration, and now we have numbers, 110 newtons minus 100 newtons is equal to the mass times acceleration. That is, of course, 10, and so we get a positive number for A. It's certainly not equal to zero, and that means that no, we are not in an inertial frame. If this was an inertial frame, [inaudible] what would the scale reading have to be? >> It would have to read 100 newtons. >> It would have to read 100 newtons. Absolutely right. And that can happen when the elevator's at rest, or when the elevator is moving with constant velocity. If it's moving up with constant velocity, then your scale reading is exactly the same as your MG, and the acceleration of the elevator is zero. And so when you think about inertial frames, just think of this. Is that frame moving at constant velocity? Now let me ask you a follow-up question. [inaudible] are you in an inertial frame right now, sitting there in your chair in this room, are you in an inertial frame? >> I would say yes, because acceleration is still in negative G. >> Okay. Are you accelerating at a negative G? >> Yes. >> You don't look like you're accelerating at negative G. >> Well, it's still pulling you down [inaudible]. >> Okay, something's pulling you down? Is it the weight of the school? All the pressure? Is that the weight? Are you accelerating right now? No. MG down, but what's pushing back up on you? >> Normal force? >> Normal force, right. So what's your acceleration right now? >> Zero. >> Zero, so are you in an inertial frame? >> No. >> Yes. You are if your acceleration is zero, but if you were moving at constant velocity, then you are in an inertial frame. Now that's, in fact, only an approximation. You in your chair in this room, moving at constant velocity, is that really right? Are we really moving at constant velocity? Is our acceleration equal to zero? >> It depends like what you're considering like relative to what -- >> Okay. >> Exactly, so in terms of like being on earth that's spinning, or rotating, then we are -- are not in inertial frame? >> Okay. Exactly right. We're sitting on the earth. The earth is spinning. We are moving in a circle right now. If you are moving in a circle, you are accelerating. You have centripetal acceleration, which means that you are in a non-inertial frame. Now that acceleration is very small compared to G, and so to a good approximation, we can say we are inertial. We are in an inertial frame. But technically speaking, it's really a non-inertial frame, because we're moving in a circle. All right. Good. Any questions about this stuff? You guys feeling okay about it? All right. If that's not clear, come see me in my office hours. Cheers.