“None of this is intuitive”

I am reminded of an oft-repeated crackpot claim that physics should be simple and intuitive, usually in terms of relativity or QM. But they are typically novices at actual physics, and probably never studied rotational systems.

(Reference: The Chewbacca defense)

This is really cool. Well, technically it’s hot.

I especially like how the drops move uphill in seeming defiance of gravity, since you can’t see the invisible transition to vapor that’s doing the work.

Veritasium has their response to the bullet/block I experiment I linked to and explained, and then explained some more. I absolutely love that they were overwhelmed with responses as people tried to figure it out.

One nit: momentum is not always, always, always, always conserved. It’s conserved when you define the system such that there is no net external force on it. The bullet-block system can be said to conserve momentum during the collision, because it happens quickly and the perturbing impulse is small. But over a longer time, the momentum clearly changes, as the block rises and then falls. One would have to incorporate the earth to have momentum be conserved, but that wouldn’t help solve the original problem. Defining the system so that one can come to a solution is a large step in the setup to any problem.

Some physics sleight-of-hand. I like it.

I have to admit, my first instinct was that the rotating block should not have gone as high, but I quickly realized why this was wrong. I don’t know if the folks in the video who are truly puzzled or acting that way for the sake of the video, because from other science videos I’ve seen, they are smart cookies.

There is not any extra energy that has to be “created” for the rotating case, because this is a completely inelastic collision. Kinetic energy is not a conserved quantity (!), total energy is. KE is only conserved in elastic collisions. There is more kinetic energy in the rotating case, and that’s just fine! And that’s the misdirection — everyone is puzzling over a quantity that’s not constant, implying that it should be. But this is why it’s a great demo — you have to identify and avoid a misconception to get the answer.

So it’s possible they are just playing to the audience to try and get you to think something mystical is going on here, or they “got it” soon after the first reaction was taped.

Now, what is conserved in these interactions is momentum, both linear and angular, since at the moment of impact there are no external forces or torques we have to worry about; we ignore gravity, since the effect during the short time of impact is very, very small. The impulse would be mgt, where t is the time of impact, and that’s small compared to the momentum of a fast-moving projectile. We’re physicists, and we set small effects to be zero. Too messy otherwise.

In the straight-on case, we have a linear momentum p, and momentum and kinetic energy have a simple relationship: KE = p^2/2m. So the kinetic energy is dictated by the momentum of the bullet (nail) just before it strikes the block, and it will go to whatever height where the energy has changes to potential energy, because in that case, mechanical energy is conserved: KE + PE is a constant when no work is done.

Concluding: If the nail has the same momentum in each case, the block must rise to the same height, rotation be damned.

Rotationally, it’s similar. The angular momentum is L = r X p, (or rp, at the point of impact), and angular momentum has a similar relation to rotational KE as the linear case does. Mass becomes moment of inertia, and you have L^2/2I as your rotational energy.

But the rotational energy does not come at the expense of the linear (which is different experience than rolling a ball or disk down an incline, where they must share). Because of the collision, KE is not conserved, and all we are doing in the rotating case is turning little less of the lost KE into sound, deformation of the wood, and a temperature increase, and using it to rotate the block.

TBA = tert-Butyl alcohol. At the triple point, where it freezes and boils at the same time.

In the last post I explained that mirrors do not flip left and right, and the example (also used in the Feynman video) was seeing an image of yourself.

I thought of another example — written words. They look backwards in a mirror as well, but if a mirror doesn’t flip left and right, how can that be? As I demonstrate, it’s because we always rotate whatever the words are written on. If we don’t do the rotation, the words are unchanged.

(I apparently started talking a second or two before the recording actually began, but this isn’t Hollywood, so I only did one take)

It may be a little tough to see the uninverted image in the mirror in the tiny youtube video, so here’s a still

A couple of things (beyond “neat video”):

He doesn’t answer the question about what would happen if you left the light on. You might think this is no big deal, because he correctly says that the light dies out quickly. If you were in a mirrored room such that the average photon trip was 3m (and somehow not interact with you at all), and the mirrors are 99.99% reflective, a photon would reflect 10^8 times a second (i.e. once every 10 nanoseconds), but only reflect 10,000 times on average, so you would expect the room to go dark in less than a millisecond. However, if you keep the light on, you get a build-up of photons for that time. To reach equilibrium, your production rate and loss rate have to be equal, and you only lose 0.01%, or 0.0001 of your photons. If you have just a 1 Watt source of visible light (which would emit around 10^18 photons a second), you need to have 10,000 times as many photons inside to have 1 Watt leaking out.
Put another way, your source is emitting 10^10 photons per bounce interval (10 nanoseconds) but only 10^6 photons leak out. In the next interval, another 10^10 photons are added and 1,000,010 photons leak out (0.0001 from each generation). And so on, with a decaying exponential buildup, until you have 10^14 photons hitting at each bounce, so that 10^10 can escape. That’s when you reach equilibrium.

So your little 1 Watt light gives you a power buildup and you are doing the equivalent of hugging 10 kW of space heaters. Actually the scenario is worse, because your body emits around 100 Watts, in the infrared, so if the mirrors reflected IR you would cook yourself to death. Fast.

The other issue I have is where he says that mirrors flip left and right and not top to bottom. The initial explanation is right — they flip perpendicular to the plane of the mirror, but then he claims that L-R is perpendicular while U-D is parallel, which is nonsense. It’s a plane, so they are both parallel. Mirrors flip front-to-back, i.e. perpendicular. The confusion is that the mental image we have is of someone walking around the mirror to the other side, and that’s not what is going on. It’s a confusion of inversion and rotation, which are two different ways of getting an image like that. There is no left-right flip! Your right hand is still on your right, it’s just that you expect it to be on your left, because of that were a person in the mirror (who has rotated on an axis to look like that), it would be their left hand.

Maybe you’ll like hearing Feynman explain it.

He loves only cold!

If you ever wondered how a Helium dilution refrigerator was, or even if you have no idea what one is, here’s a great explanation.

Associate Professor Andrea Morello from the University of New South Wales explains how ‘zero-point motion’ makes it possible to use Helium-3 and Helium-4 in a dilution fridge to get down to only thousandths of degrees above absolute zero.
It is this technique which is used to cool the MiniGrail at Leiden so that it can act as a gravitational wave antenna.