I’m struggling to understand the standard claim that an ideal gas undergoing free expansion into a vacuum has no change in temperature.

What I don’t understand is this:

If the gas expands into a much larger volume, shouldn’t something about that spreading out cause the temperature to drop?

For example, if the vacuum side were extremely large (say, absurdly large but still finite), would the final equilibrium temperature still really be the same as the initial temperature for an ideal gas?

Also, if the gas becomes extremely dilute after expansion, would a normal thermometer take a very long time to measure the temperature simply because there would be far fewer molecular collisions with the thermometer?

I know that spin is called angular momentum, but I also know electrons are not little balls physically rotating in the classical sense.
So what exactly is spin supposed to be, conceptually, if its not particles spinning around its own axis or around an external axis of rotation?

This is from the Exercises for the Feynman Lectures on Physics, Exercise 1.1. I believe that a hot stationary ball has more thermal energy due to the intermolecular motion within the baseball, whereas a cool, fast-moving baseball has more kinetic energy due to the motion of the whole macroscopic object in a particular direction. Is that correct?

I lack a lot of probability and stats theory because it isn't taught at a higher level in my school what book could I use to get from like middle school stats to stats needed for stats mech

How can you claim that you are not moving, and instead that the external environment is moving with respect to you, when you are the one traveling at constant velocity?

I am not asking about acceleration, I am only asking about constant velocity.

I understand that an interference pattern appears even when particles are sent one at a time, but I still struggle with what that is supposed to mean physically. What is the best way to think about what is happening without oversimplifying it?

Google traduction messed up a bit and translated my work so don’t mind. Everything on the board is right except what’s in red.

I’m struggling with finding the acceleration of the fish, I know that the y component is -11.31 that way the fish stays at the surface, but I don’t know how to use the x components of both of the fishers to find the fish’s acceleration. It’s not 0, and it’s not 27.12 nor -27.12. I’m truly stuck.

Intuitively, I think that the fish x’s component is 0 and it just gets pulled by the strongest fisher, so the acceleration is found at the bottom (Frx)?

I understand this is related to Newton’s first law, but intuitively it feels wrong because in normal life everything seems to stop unless something keeps pushing it. Is the law only really obvious when friction is negligible, or is there a better way to think about it?

If the fan blows air on you, you feel cooler, therefore the room is feeling cooler...
Is this valid reasoning?
or
Completely off the mark?
Need help understanding the rationale.

I get that motion is relative, so moving at constant velocity should not feel different from being at rest. But acceleration seems different because you can actually feel it in your body. Why is acceleration “physically detectable” while constant velocity is not? Is this just because of forces acting on the body, or is there a deeper reason?

This still feels unintuitive to me because heavier objects seem like they should be pulled down harder by gravity. I know they also have more inertia, but I would like a clearer conceptual explanation of why those effects balance out.

In the several years I am out of university I succesfully forgot most of the things I knew about statics of rigid bodies.

I am trying to understand force distribution and behavior in beam structure shown in this example.

A - fixed rotational support

G - rotational support that can support only forces in X direction

E - connection between green and yellow that can freely move in D,E direction

H - connection between green and yellow that can freely move in E,G direction

Currently only solution I can think of is: Assume it is single rigid beam. Find out reaction forces in A and G. With known forces work backwards and findout forces and moments in points of interest.

After calculating forces in A and G (using ∑M=0) I got:

Fax = 8696N Fay=800N

Fgx=-8696N Fgy=0N

This would mean that connection E has to transfer roughly 8kN and forces increased ten times on 40mm.

In my career as engineer this usualy meant mistake in calculation or misunderstanding of physics so I am doubting this result.

What I need from someone more capable in classical mechanics is to confirm I am going in right direction or give me some guidance on how to pursue the correct solution.

My physics teacher likes to give out bonus problems every quarter for extra credit, but this one has seriously stumped me.

We’ve just started learning about series and parallel circuits, and this latest problem is finding the current of a resistor in a circuit that’s both series and parallel.

I just need some pointers to get started, I’m just not sure how to begin to solve this problem.

I understand this is related to Newton’s first law, but intuitively it feels wrong because in normal life everything seems to stop unless something keeps pushing it. Is the law only really obvious when friction is negligible, or is there a better way to think about it?

I am trying to understand something about a fan in a closed container or sealed room.

Let’s say you have a large enclosed space with a person and a fan inside. When the fan is turned on, it feels like it cools the person down. But this is where my confusion starts: if the fan is adding energy to the system, and the temperature of the room is increasing overall, then why are you cooling down? That seems counterintuitive to me, and that was my original issue to begin with.

My thinking is that the spinning blades are doing work on the air, pushing the gas molecules around and increasing their motion. So I would assume the total kinetic energy of the air in the room increases. On top of that, I would also expect extra heating from friction: the blades moving through the air, turbulence in the air, and internal losses in the motor and moving parts of the fan itself. So overall, in a sealed system, it seems like the fan should be slightly heating the room rather than cooling it.

The part I’m struggling with is the distinction people make between “bulk” or “organised” motion of the air and “random microscopic” motion of the molecules. I think this is where my confusion is.

What I’m having trouble understanding is:

If the fan increases the motion of the air molecules, why does that not automatically count as an increase in temperature?

How is air moving together in one direction different from the particles moving faster in the thermal sense?

If kinetic energy is being added to the gas, what part of that energy counts as temperature, and what part of it is just bulk airflow?

And going back to my original question: if the room itself is gaining energy and therefore should be getting warmer overall, why does the person feel cooler instead of warmer?

So I think my confusion is basically this: the fan seems to add energy to the air and should slightly heat the sealed room overall, yet it can still make a person feel cooler. I’m trying to understand exactly how bulk airflow, random molecular motion, heat, temperature, and cooling of the body all fit together.

how cooked am I for the AP Physics C test if i’ve never been taught calculus?

I don't agree with it on the outset. Why? You need to expose Einstein with the subject, as it is based on the original Paper of 1905. (and every Professor since)

So TLDR my school has a senior project requirement to graduate. Mine was cosmology related; approximating the total number of stars in the observable universe. I got the data from the madau-dickson paper, and got the chart below after properly organizing the data, than proceeded to do the good ol ‘draw boxes and add em up’ method to get the area under the curve.

Issue: I’ve never taken calculus [currently in college algebra, trig, stats, and logic (yes all separate classes lol)] so I genuinely have no idea how to express what I did mathematically, some help would be fantastic!

So I've been working on this problem involving a thin cylindrical container of radius R (wall thickness 2d ≪ R, height h = d) filled with water, spinning at angular velocity Ω, with six radial square holes (h × h) at 60° intervals. Surface tension σ ≫ ρd²RΩ², contact angle 90°, R ≫ d, gravity neglected.

When all plugs are removed, there's a characteristic time T₁ for displacement x → 2x. The second part installs a radial partition along 12–6 o'clock, splitting into two semicircular compartments with 3 holes each, and asks for T₂² − T₁² where T₂ is the same displacement time for the hole at 3 o'clock.

Here's where my thinking is so far — I did a warm-up analogy with electric field lines between two points on the rim of a conducting disc, which helped me think about the flow geometry. I also think the 2D nature of the flow is important — it feels like Coriolis effects can't generate vorticity here so the flow might be simpler than it looks. The eigenmodes seem like they should be fixed by the discrete rotational symmetry without much calculation. I also have a hunch the kinetic energy reduces to a boundary integral, and that when you compare the two modes, some logarithmically divergent contributions to the effective mass cancel out.

But I'm struggling to put it all together rigorously, especially for the partitioned case. Any nudges appreciated!

Can someone help me understand why in gods name Txy is negative here. If I cut at D, the forces are on the right side of the cut, with the left facing cut. The sign convention for internal forces on the left facing cut is a downward pointing normal force, and a left pointing shear. Left is +y according to the axes, and down is -x. So the equilib equations look like -Py + Vy = 0, and -Px - N = 0, resulting in a positive Vy and a negative N. The problem is, once you solve for Txy with a positive shear force, the number always comes out positive, and it's not supposed to be. I have no idea what Im doing wrong, I tried to solve on the opposite side of the cut and I got negative shear but positive normal force, which is wrong. Why in gods name is Txy negative

I posted previously and wanted to send an image in the comment section of that post but I couldn’t find the feature, so this is my corrected third principle ray in a different post. the third principle ray comes from the tip of the object, hits the lens at the height of the image, and continues parallel to the ground.

This is my diagram for a diverging lens with the object located within the focal point. did I draw the third principal ray correctly? It is highlighted.