thanks 😂

i am smooth enough (pun intended)

wow my comment was mentioned too

A merry everything and a happy always stackers! May you stack more sats than Santa's sack of toys this year 🎄🎅🤶❄

To the moon in '25, one day bitcoin will reach that height :)
Merry Christmas! Stack sats, Stay humble

Tom Holland as Telemachus ❌
Tom Holland as Tom Holland ✅

worth the read

compared to other fields of physics, quantum is still a baby learning its steps, it will require at least 100 more years of research to get it to some understandable level, preferably more work on time, light and gravity

ohhh

so that means new items will be more visible easily somehow on the top page even if it persists for a small time?

I was as old as 18 when I was Jimmy's age.

This was really an interesting read! I remember this discussion by my own physics teacher.

• Earlier theories proposed that pressure from a skate or foot lowers ice's melting point, creating a water film, as suggested by James Thomson in the 1800s.
• Frictional heating from motion was another idea, where rubbing generates enough warmth to melt the surface slightly. Experiments, like those by Lord Kelvin, supported friction's role by showing higher friction with heat-conducting materials. We also have the theory of pre-existing quasi-liquid layer (QLL) on ice surfaces, formed by weaker bonding of surface molecules exposed to fewer neighbors

But I think we already have a reasonable solution to this problem through dipole interactions which says molecular dipoles in ice align and disrupt with those in contacting surfaces like shoe soles, disordering the ice into a slippery, amorphous state without needing heat or pressure. This viscous, oil-like film resembles crushed ice in snow cones, enabling low friction. Although the explanation for regelation of ice still remains unattended in this case. [EXPLANATION]

and then we have lie algebra too, recently there was a post about the nopertahedron breaking the rupert theorem which was related to this. I remember discussing with @carter about Lie algebra tho

looks worthy of reading, i must try it

excellent! Correct steps too!

Congo to @SHA256man for this weeks BNB 🥳!

Here is the detailed solution in case some don't understand:

Given:Given:

• Mass of box on incline: $m$
• Incline angle: $\theta$
• Hanging mass: $M$
• Pulley: frictionless bearing but with moment of inertia $I$ and radius $R$ (to be included for rotational effects)
• Rope: light and inextensible
• The system is released from rest at $t=0$
• Incline is frictionless

Okay so,

• Let acceleration of box along the incline be $a$ downwards (positive direction along slope down).
• The hanging mass moves vertically downward with acceleration $a$.
• Let tensions on the box side of the rope and hanging mass side be $T_1$ and $T_2$ respectively.
• Because the pulley has rotational inertia, $T_1\ne T_2$.

(Box accelerates down the incline, gravity component downward minus tension force opposing motion.)

(Mass accelerates downwards, gravity downward minus tension upward.)

Since the rope unwinds without slipping, the angular acceleration $\alpha$ of the pulley relates to linear acceleration $a$ by:

Torque $\tau$ on pulley is caused by difference in tensions:

Rearranged:

We have 3 equations:

1. $ma=mg\sin \theta -T_1$
2. $Ma=Mg-T_2$
3. $T_2-T_1=\frac{I}{R^2}a$

Rewrite tensions from (1) and (2):

Substitute into (3):

Simplify:

Group terms with $a$ on right:

• If pulley moment of inertia $I=0$, this reduces to a simpler formula:

(This case may be problematic if $M=m$, implying infinite acceleration—showing the importance of pulley inertia.)

• If the pulley has significant $I$, the denominator increases, reducing acceleration. :)

lol true

no but the pulley is a frictionless bearing but with moment of inertia I and radius R (to be included for rotational effects)

it actually is cheap

true.
those who can't make love make war.

Even about ~5 years back this was a popular notion that particles were being made from waves or light with fields whose excitations manifest as particles. But modern physics has changed the viewpoint, as far as I know, electrons are fundamental particles, so they aren’t made of anything. They’re excitations of the electron field (not to be confused with the electric field).

If had to explain, in an atom the electron field gets the localized shape it has because there are also nearby excitations in the quark field (in the nucleus). The quarks are charged and interact with the electromagnetic field, which also interacts with the electron field.

So you basically have three fields at play here: quark field, electron field and electromagnetic field. They all interact together such that they each get a particular "shape".

What we mean by "interact" is that mathematically the value of one field depends on the value of another field.

In Quantum Mechanics (actually Quantum Field Theory) the "value" of a field is something a bit more abstract than e.g. a single scalar number or vector quantity - instead the "value" is called a "state". I can't really explain what a "state" is in QFT so easily without the Bra-ket, except that it is indeed the mathematical "object" that fully describes what state or configuration the field/particle is in.

It might not be a SCT/MCT. I want to SEE, I'm not into astrophotography....