How do i gain intuition to learn and remember physics?

Throughout my life, most of the things I've learned have come naturally, and seem to commit to memory without the need for much effort.



However now while I'm in the process of self-studying math and physics, i find that i constantly seem to forget everything i learn and can only make progress by making rigorous use of memorization techniques and disciplined note review.



However i had been hoping to just read physics materials and naturally absorb content and get an intuitive feel for it overtime, as note taking and the need for memorization techniques kind of suck the joy out of the process.



The problem is i feel like I'm just reading a bunch of random facts and equations and cant solidify or connect the information in some meaningful structure, so i keep forgetting it all.



I also forget because many of the equations seem to make no intuitive sense to me so i cant deduce them in practical situations.



i.e. I have no idea why centripetal acceleration is velocity times itself and then divided by the radius.



So i suppose my questions are:



1. Does anyone have an alternative perspective or mental framework they could suggest which would help me latch on to, intuitively understand, and categorize physics concepts more efficiently?

2. How can i get a better natural intuition/understanding for equations?

Why do I just not "get" math proofs?

The only proof-based math class I've taken so far was on abstract algebra. Concepts were easy for me to understand, but I was constantly having trouble with some of the proofs.



I so frequently get this feeling that the last, tiny trivial step left in my proof is just "right there," and yet I can't find it. Or I might drastically over-complicate things and write a page proving something that my professor's solution states in one line as an obvious conclusion (which it was). It's just ridiculous; there were a few problems assigned for the class that I might spend four hours just messing around with until finally figuring out a convoluted (though valid) proof to when they could have been solved in a few lines.



Technically, grade-wise, I did well in the class, but in the end, I still feel like proof-writing just doesn't come naturally to me. Now I'm working on learning topology and differential geometry, and while, again, I can understand the concepts and proofs and do some of them on my own, none of the proofs ever come naturally to me.



Honestly, is it common for people to take so long to get used to writing proofs? I'm just working on getting the hang of things (self-studying topology and differential geometry now) but it's not really happening.

To find the current through an inductance in an AC circuit.

1. The problem statement, all variables and given/known data

An inductance is connected across an AC current generator.





2. Relevant equations

v= L di/dt = Vsinωt





3. The attempt at a solution



i=∫di= V/L ∫sinωt dt= -V/ωL cosωt





This is what is written in my book. But wouldn't there be a constant at the end of the indefinite integral?

Revolution problem

Can someone please show me how to do this? I usually don't ask for answers and try to work it out myself but I just cannot figure this out I've tried everything. And please explain why you solve it the way that you do.



Region bounded by y= sqrt x y=0 x=0 about x=4 the answer is supposed to be 224pi/15

Self locking gears for parabolic solar concentrator

Hello everyone, my question is: Would be ok to use a self locking gear like a worm gear for a solar tracker system on a 2 ton parabolic mirror dish? Would it be necessary some kind of brake system, or the worm gear would be enough?



If so, are there any type of self locking gears besides the worm gear?. The idea to use a self locking gear is to stop the dish at a certain position and angle, so that the dish is perpendicular to the sun, and the lock would stop the inertial load (parabolic dish) from back driving the system.



Also I have been thinking about the garage door opener systems, does anyone know how the system is locked and cannot be opened by simply pushing or pulling the door? Is the worm gear the thing that make it impossible to open the door by force?



If you have had experience in positioning systems like big satellite dishes, antennae or parabolic solar concentrators (Solar trackers) what would be your suggestion to drive the system (actuators and transmission mechanism).



Thank you in advance for your time.



RM

Probability of finding a system an eigenstate

1. The problem statement, all variables and given/known data



As the homework problem is written exactly:

Consider the quantum mechanical system with only two stationary states |1> and |2> and energies E₀ and 3E₀, respectively. At t=0, the system is in the ground state and a constant perturbation <1|V|2>=<2|V|1>=E₀ is switched on. Calculate the probability of finding the system in the state |2>.



2. Relevant equations

H=V (I'm just assuming these states must be such that there is no kinetic energy and E=V, but that's just my guess - professor lacks communication skills at times).



|c₁|² + |c₂|² = 1

P(|2>)=|c₂|² (thus, I need c₂ to solve the problem!)



3. The attempt at a solution

Well, I'm completely confused as to why he gave us <1|V|2>=<2|V|1>=E₀, what that even means, and where I'm supposed to retrieve the probability coefficients which is all I need to solve the problem.

Mechanics calc physics question

1. The problem statement, all variables and given/known data

Grains of fine California beach sand are approximately spheres with an average radius of 50 μm and are made of silicon dioxide, which has a density of 2.5 × 103 kg/m3. What mass of sand grains would have a total surface area (the total area of all the individual spheres) equal to the surface area of a cube 0.9 m on an edge?





2. Relevant equations

density=mass/volume

surface area of sphere=4(pi)r^2

volume of sphere= (4/3)(pi)r^3





3. The attempt at a solution

My attempt at the solution was i plugged 0.9 into the surface area equation and solved for the value r which gives the surface area equaled to 0.9. I then used the r that i calculated for and plugged that into the volume equation to get the value of V to then plug that into the density equation to find the mass using the given density of the sand and the volume from what i calculated. I do not know where the 0.5μm and i think that is the problem i am having. FInal answer i got was 200kg?

Help Developing My Senior Physics Project Concept

Hello. I am an undergraduate physics major and am struggling to identify a senior project research question that I can pursue over the next 2 semesters. I already opted to do my project on heliophysics, but that is obviously a rather broad subject.



While doing general reading, I came up with a couple of thoughts, but I don't know how viable they are as projects:



- How is the solar spectrum that we see (or can't see for those wavelengths outside of the visible) on Earth different from what a satellite sees, or from the wavelengths that are actually produced within the Sun itself? What goes on between the production of a photon in the Sun and its arrival on Earth, in terms of redshift, scattering, absorption, the interference of Earth's magnetosphere, and so on, and when physicists study the Sun through its spectrum, do they need to compensate for any of these things?



- What does the magnetic field of our Earth-Sun system look like, and how does the field of the Earth interact with the field of the Sun? For instance, as an example of semi-indirect interaction, the Sun's magnetic field is believed to be responsible for coronal mass ejections that, when the Earth is in their path, "collide" with Earth's magnetosphere and produce the polar lights. How do physicists model these fields and events?



To complicate matters, I have a physical disability that prevents me from collecting my own data or conducting my own experiments. I don't know what to do about that, because while I would happily write a 25 page "review of the literature", this project is meant to be experimentally based, and is restricted to 5 pages of text besides.



I would appreciate any advice on how I can develop either of my ideas into a real project (or the blunt truth that they are both bad and/or erroneous, if that is the case). Thank you for taking the time to read my rather long explanation.

OSCILLATING my brain

i know this problem is posted on this forum somwhere else but i cant quite understand thanks in advance



1. The problem statement, all variables and given/known data



A mass of 0.3 kg is suspended from a spring of stiffness 200 N m–1. If

the mass is displaced by 10 mm from its equilibrium position and

released, for the resulting vibration, calculate:



the maximum velocity of the mass during the vibration



2. Relevant equations



F=kl







3. The attempt at a solution



so far i am thinking that i need to use hookes law as follows so i can get the amplitude

F=k(l+x)



F= mg = 0.3 kg x 9.81 = 2.94 N

k = 200 Nm^-1

l = static spring reflection = 2.94/200 = 0.01

x = displacement due to external force = 10mm



so the amplitude would be l + x = 10.01mm?



do i need to take into account the extra extension when attempting the solution or is it just f/k =l

or do i need to use f/k = l + x to calculate the amplitude





any help would be appriciated



Thanks

Capacitive Coupling Issue

I have an FPGA demo board and on the GPIO I have attached a 4 x 3 membrane keypad. This keypad is simple, create a current on the column pins and look for a completed circuit on the row pins.









At the minute, I just having it driving a bunch of LEDs to indicate what has been pressed. I have written the VHDL code for this and it appears to be working fine.



My problem is that if I bring my hand within 15cm of the keypad, the LEDs start to light up. So, I am coupling with the circuit and bridging the switches. I dropped the frequency from 2MHz to 1KHz to try to resolve it, but no luck. I can move my hand around the keypad and cause different LEDs to light up.



Does anyone have a resolution for me?

Error 112 FORTRAN95

Hi,

I'm new in this space, I have a problem building a program with Fortran95 (I'm also new on this). The program it's really easy, I have to make a random generator using RANMAR subroutine here is the code:



program random

use aleatorio; use SAVEDATA

Implicit none

real, allocatable :: V(:)



integer N



write(*,*) "Choose the numbers"

read (*,*) N



allocate (V(N))



call RANMAR (V,N)



write(*,*) "Numbers:",V



call keep()

deallocate (V)

stop

end program random



module SAVEDATA





contains



subroutine keep()



real, allocatable :: V(:)

integer N



integer :: i

character (len=30)::fileb



write (*,*) 'what is the name of your file?'

read (*,*) archivo



open (10,file=fileb, access='append')

do i= 1,N

write (10, *) V(i)

enddo



end subroutine keep

end module SAVEDATA



I've got problems with this subroutine, the other one works! here is the error warning:



Run-time Error

*** Error 112, Reference to undefined variable, array element or function result (/UNDEF)



SAVEDATA!KEEP - in file salvar.f95 at line 24 [+019c]



main - in file main.f95 at line 29 [+031a]



If somebody could tell me something about it, I'd be so thankful.



SPELUX11

String supports disk

A disk of mass M and radius R is held up by a massless string. (The two ends of the string are connected to a ceiling and the disk rests on the bottom of the string.) The coefficient of friction between the disk is μ. What is the smallest possible tension in the string at its lowest point?



This is from "Introduction to Classical Mechanics" by David Morin. I am confused as to how T(∏/2) = Mg/2. T(∏/2) refers to the tension in the rightmost point of the disk where the string does not touch the disk anymore.)

Getting two difference results when calculating volume of cylinder?

This actually isn't a homework problem -- I'm just trying to understand an example in my textbook. The example shows how to calculate the volume of a cylinder (maybe it's actually a shell, I'm not sure) using an integral, but it occurred to me that I should be able to simply "unwrap" the cylinder so that it's just a rectangle and then multiple the dimensions instead of integrating.



For some reason the answers are not the same, and I don't understand why. Here's my work:







What did I do wrong?

Electrostatic voltage and current

If we had a van de graaff generator, near the sphere there is a metal plate ( not touching) and it's wired to the ground (a resistor is connected to the wire) , as the voltage on the surface of the sphere increases, the voltage at the plate does too, creating a potential difference between the plate and the ground and a current will flow, will this current depend on the resistance of the wire? ( no electrical discharges occurs )

Probelm with modelling a triangle

Hi,

i am trying to model a triangle in a square cell based on its dimension. However, i have some problem with parts of the code, i think it might be the logic behind my programming or over definition with the code itself.



i have attached the code. the problem lies with the second half of the triangle. I have also attached the basis of my analysis. the problem lies between -s/2 to s/2 of the code. Any hints about the wrong logic of my code or over definition will be appreciated. the cell is a square dimension with 2r1x2r1 dimension.



I have attached the matlab code and the definition of the cell if you are interested.

Attached Images

20140901_011337158_iOS.jpg (60.4 KB)

Attached Files

triangle_90_deg_surface_step_bottom.m (7.3 KB)