Prof. Walter Lewin Teach Rotational K.E at MIT

Added: 2026-06-03

[00:00:00]speed that the person could use is at most 10 miles per hour without killing him or herself, which is about 4 m/s.

[00:00:13]And so here's your car and let's assume you start out with zero speed and let's assume that the mass of the car will give it nice numbers is just 1,000 kg. And so you zigzag down this road.

[00:00:28]Uh let us assume that the height difference H let's give it a number 500 m and you arrive here at point P and you later have to go back up again. What is your kinetic energy when you reach point P? Well, you have a speed of 4 meters/s and as you went down, you've been breaking all the time. One way or another, you got rid of your speed and that's all burned up heat. you heat up the universe. So when you reach point P, your kinetic energy at that point P is simply 12 M V ^ 2. M is the mass of the car. So that is 500 * 16 V ^ 2. So that is 8,000 Jew.

[00:01:14]Now compare this with the work that gravity did in bringing this car down.

[00:01:20]That work is mgh.

[00:01:23]And mgh is a staggering number. 1,000 * 10 * 500 that is 5 million jewles and all of that was converted to heat using the brakes. It actually even gives you also wear and tear on the brakes. So who needs it? Is there perhaps a way that you can salvage it or maybe not all of it, maybe part of it? And the answer is yes, there are ways. At least in principle, there are ways. You can install a disc in your car, which I would call then a flywheel, and you can convert the gravitational potential energy.

[00:02:03]You can convert that to kinetic energy of rotation in your flywheel.

[00:02:08]And to show you that it is not completely absurd, I will put actually in some numbers. Suppose you had a a disc in your car which had a radius of half a meter. That's not completely absurd. That's not beyond my imagination. That's it's a sizable disc and I give it a modest mass so that the mass of the car is not going to be too high. 200 kg that's reasonable. That would be a steel plate only 5 cm thick but that's quite reasonable. And the moment of inertia of this disc if I rotate it about an axis through the center perpendicular to the disc that moment of inertia we know now is 12 m.

[00:02:47]Oh, we have a capital M R 2 and that equals 25. The units are kilograms if you're interested. kilograms a meter squared.