1 00:00:00,270 --> 00:00:03,060 ‫Welcome back, and here you have the answers. 2 00:00:03,240 --> 00:00:10,650 ‫This is your first position vector for June one and this is your second position vector for June two. 3 00:00:11,100 --> 00:00:19,770 ‫As you can see, you have to pay attention to the direction of each inertial frame dimension in order 4 00:00:19,770 --> 00:00:23,280 ‫not to mess up the plus and minus signs. 5 00:00:23,550 --> 00:00:29,460 ‫And also, I could have put that inertial frame in any other place. 6 00:00:29,820 --> 00:00:35,820 ‫I could have put it here or here or here or even here. 7 00:00:36,330 --> 00:00:43,410 ‫And with each choice, the position vectors would have been different because you would be measuring 8 00:00:43,410 --> 00:00:46,200 ‫the distances from a different location. 9 00:00:46,890 --> 00:00:51,150 ‫Now, there is one final remark that I want to make about the inertial frames. 10 00:00:51,480 --> 00:00:59,580 ‫When we say that an object moves with respect to an inertial frame, it means that the object moves 11 00:00:59,790 --> 00:01:07,260 ‫along with the body frame and the inertia frame is fixed to the ground or to the building or wherever 12 00:01:07,260 --> 00:01:08,440 ‫you fix it to. 13 00:01:08,670 --> 00:01:10,560 ‫So the initial frame is not moving. 14 00:01:10,920 --> 00:01:18,630 ‫However, then you could say that, OK, but the ground is not fixed because the ground is on the planet 15 00:01:18,630 --> 00:01:21,350 ‫Earth and the planet Earth rotates. 16 00:01:21,750 --> 00:01:26,780 ‫So why wouldn't we use the center of the Earth as our inertial reference frame? 17 00:01:27,120 --> 00:01:35,490 ‫However, the Earth rotates around the sun and the sun rotates around the black hole in the middle of 18 00:01:35,490 --> 00:01:42,440 ‫the Milky Way galaxy, and even our galaxy moves with respect to other galaxies. 19 00:01:42,870 --> 00:01:46,680 ‫So it seems that in our universe there is nothing fixed. 20 00:01:46,680 --> 00:01:47,850 ‫Everything moves. 21 00:01:48,300 --> 00:01:58,440 ‫But the point is what moves with respect to what if I put my reference frame onto the ground and fix 22 00:01:58,440 --> 00:02:07,380 ‫it to some kind of location, then yes, that location moves with the earth, but so does the car and 23 00:02:07,380 --> 00:02:10,010 ‫the drone when they are completely at rest. 24 00:02:10,140 --> 00:02:17,430 ‫When the drone or the car, when they don't move at all, then their location with respect to that inertia 25 00:02:17,430 --> 00:02:19,860 ‫frame location doesn't change. 26 00:02:20,220 --> 00:02:28,110 ‫And both the inertial frame and then the body frame attached to a drone or a car or or another object, 27 00:02:28,440 --> 00:02:35,250 ‫all of them rotate around the center of the earth and around the sun and around the center of the galaxy 28 00:02:35,550 --> 00:02:37,430 ‫and with respect to other galaxies. 29 00:02:37,800 --> 00:02:41,310 ‫So it's all about what moves with respect to what. 30 00:02:41,610 --> 00:02:49,020 ‫And depending on the problem that you have to solve, you have to find for yourself the most convenient 31 00:02:49,230 --> 00:02:52,140 ‫location for your inertial reference frame. 32 00:02:52,500 --> 00:02:59,700 ‫If you have a car that wants to change the lane or you have a drone that wants to fly close to you, 33 00:03:00,180 --> 00:03:07,860 ‫then choosing some kind of ground location for your inertial frame that is close to that car or drone 34 00:03:08,280 --> 00:03:09,180 ‫makes sense. 35 00:03:09,360 --> 00:03:16,980 ‫But of course, if you have a long distance flight with an airplane or a satellite orbiting the Earth, 36 00:03:17,370 --> 00:03:23,010 ‫then perhaps it is better to choose the center of the Earth as the location for your inertia frame. 37 00:03:23,400 --> 00:03:31,920 ‫And if you have interplanetary travels, then perhaps the center of the sun could be a good place for 38 00:03:31,920 --> 00:03:32,240 ‫that. 39 00:03:32,370 --> 00:03:36,120 ‫So it all depends on the problem that you have to solve. 40 00:03:36,450 --> 00:03:43,980 ‫And then you choose a location for your inertia frame, which makes sense and which is suitable for 41 00:03:43,980 --> 00:03:45,680 ‫that specific problem. 42 00:03:46,200 --> 00:03:48,030 ‫So that's what I wanted to mention. 43 00:03:48,240 --> 00:03:52,400 ‫And now in the next video, we're going to start talking about rotation matrices. 44 00:03:52,830 --> 00:03:53,880 ‫Thank you very much. 45 00:03:53,880 --> 00:03:54,720 ‫And see you there.