Physics

Topic

First Poster

Last Poster

k a April Highlights and 2025 AoPS Online Class Information

jlacosta 0

Apr 2, 2025

Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.

Looking for summer camps in math and language arts? Be sure to check out the video-based summer camps offered at the Virtual Campus that are 2- to 4-weeks in duration. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

Be sure to mark your calendars for the following events:
[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
[*]April 8th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS State Discussion
April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
[*]April 10th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MathILy and MathILy-Er Math Jam: Multibackwards Numbers
[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

Introductory: Grades 5-10

Prealgebra 1 Self-Paced

Prealgebra 1
Sunday, Apr 13 - Aug 10
Tuesday, May 13 - Aug 26
Thursday, May 29 - Sep 11
Sunday, Jun 15 - Oct 12
Monday, Jun 30 - Oct 20
Wednesday, Jul 16 - Oct 29

Prealgebra 2 Self-Paced

Prealgebra 2
Sunday, Apr 13 - Aug 10
Wednesday, May 7 - Aug 20
Monday, Jun 2 - Sep 22
Sunday, Jun 29 - Oct 26
Friday, Jul 25 - Nov 21

Introduction to Algebra A Self-Paced

Introduction to Algebra A
Monday, Apr 7 - Jul 28
Sunday, May 11 - Sep 14 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Wednesday, May 14 - Aug 27
Friday, May 30 - Sep 26
Monday, Jun 2 - Sep 22
Sunday, Jun 15 - Oct 12
Thursday, Jun 26 - Oct 9
Tuesday, Jul 15 - Oct 28

Introduction to Counting & Probability Self-Paced

Introduction to Counting & Probability
Wednesday, Apr 16 - Jul 2
Thursday, May 15 - Jul 31
Sunday, Jun 1 - Aug 24
Thursday, Jun 12 - Aug 28
Wednesday, Jul 9 - Sep 24
Sunday, Jul 27 - Oct 19

Introduction to Number Theory
Thursday, Apr 17 - Jul 3
Friday, May 9 - Aug 1
Wednesday, May 21 - Aug 6
Monday, Jun 9 - Aug 25
Sunday, Jun 15 - Sep 14
Tuesday, Jul 15 - Sep 30

Introduction to Algebra B Self-Paced

Introduction to Algebra B
Wednesday, Apr 16 - Jul 30
Tuesday, May 6 - Aug 19
Wednesday, Jun 4 - Sep 17
Sunday, Jun 22 - Oct 19
Friday, Jul 18 - Nov 14

Introduction to Geometry
Wednesday, Apr 23 - Oct 1
Sunday, May 11 - Nov 9
Tuesday, May 20 - Oct 28
Monday, Jun 16 - Dec 8
Friday, Jun 20 - Jan 9
Sunday, Jun 29 - Jan 11
Monday, Jul 14 - Jan 19

Intermediate: Grades 8-12

Intermediate Algebra
Monday, Apr 21 - Oct 13
Sunday, Jun 1 - Nov 23
Tuesday, Jun 10 - Nov 18
Wednesday, Jun 25 - Dec 10
Sunday, Jul 13 - Jan 18
Thursday, Jul 24 - Jan 22

Intermediate Counting & Probability
Wednesday, May 21 - Sep 17
Sunday, Jun 22 - Nov 2

Intermediate Number Theory
Friday, Apr 11 - Jun 27
Sunday, Jun 1 - Aug 24
Wednesday, Jun 18 - Sep 3

Precalculus
Wednesday, Apr 9 - Sep 3
Friday, May 16 - Oct 24
Sunday, Jun 1 - Nov 9
Monday, Jun 30 - Dec 8

Advanced: Grades 9-12

Olympiad Geometry
Tuesday, Jun 10 - Aug 26

Calculus
Tuesday, May 27 - Nov 11
Wednesday, Jun 25 - Dec 17

Group Theory
Thursday, Jun 12 - Sep 11

Contest Preparation: Grades 6-12

MATHCOUNTS/AMC 8 Basics
Wednesday, Apr 16 - Jul 2
Friday, May 23 - Aug 15
Monday, Jun 2 - Aug 18
Thursday, Jun 12 - Aug 28
Sunday, Jun 22 - Sep 21
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)

MATHCOUNTS/AMC 8 Advanced
Friday, Apr 11 - Jun 27
Sunday, May 11 - Aug 10
Tuesday, May 27 - Aug 12
Wednesday, Jun 11 - Aug 27
Sunday, Jun 22 - Sep 21
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)

AMC 10 Problem Series
Friday, May 9 - Aug 1
Sunday, Jun 1 - Aug 24
Thursday, Jun 12 - Aug 28
Tuesday, Jun 17 - Sep 2
Sunday, Jun 22 - Sep 21 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Monday, Jun 23 - Sep 15
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)

AMC 10 Final Fives
Sunday, May 11 - Jun 8
Tuesday, May 27 - Jun 17
Monday, Jun 30 - Jul 21

AMC 12 Problem Series
Tuesday, May 27 - Aug 12
Thursday, Jun 12 - Aug 28
Sunday, Jun 22 - Sep 21
Wednesday, Aug 6 - Oct 22

AMC 12 Final Fives
Sunday, May 18 - Jun 15

F=ma Problem Series
Wednesday, Jun 11 - Aug 27

WOOT Programs
Visit the pages linked for full schedule details for each of these programs!

MathWOOT Level 1
MathWOOT Level 2
ChemWOOT
CodeWOOT
PhysicsWOOT

Programming

Introduction to Programming with Python
Thursday, May 22 - Aug 7
Sunday, Jun 15 - Sep 14 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Tuesday, Jun 17 - Sep 2
Monday, Jun 30 - Sep 22

Intermediate Programming with Python
Sunday, Jun 1 - Aug 24
Monday, Jun 30 - Sep 22

USACO Bronze Problem Series
Tuesday, May 13 - Jul 29
Sunday, Jun 22 - Sep 1

Physics

Introduction to Physics
Wednesday, May 21 - Aug 6
Sunday, Jun 15 - Sep 14
Monday, Jun 23 - Sep 15

Physics 1: Mechanics
Thursday, May 22 - Oct 30
Monday, Jun 23 - Dec 15

Relativity
Sat & Sun, Apr 26 - Apr 27 (4:00 - 7:00 pm ET/1:00 - 4:00pm PT)
Mon, Tue, Wed & Thurs, Jun 23 - Jun 26 (meets every day of the week!)

0 replies

jlacosta

Apr 2, 2025

0 replies

J

H

i A Comprehensive List of Physics Olympiad Resources

Lol_man000 177

N Aug 13, 2024 by enya_yurself

A Comprehensive List of Physics Olympiad Resources

Before I start, I would advise everyone to read this link for lots of advice on starting and learning physics.

Updates

Introductory Physics Books
[list]
[*] Physics by Halliday Resnick Krane (Calculus-based) Harder version of HRW with about 1/3 more harder material added to each chapter. Previous editions were edited by former USAPhO coach. This book covers almost all the material required for physics olympiads and is recommended by many coaches and teachers alike.
[*] Fundamentals of Physics by Halliday Resnick Walker (Calculus-based). Easier version of Halliday Resnick Krane (HRK, see above).
[*] Physics: Principles with Applications by Giancoli (Algebra-based)
[*]Physics for Scientists and Engineers by Randall D. Knight (Calculus-based).
[*] University Physics by Young. Similar to HRK, it covers a lot of the first year undergraduate sequence and contains loads of information.
[/list]

Subject Specific Books
[list]
[*] An Introduction to Classical Mechanics by David Morin. Comment (USAPhO/IPhO, some chapters are relevant to F=ma practice)

[*] Electricity and Magnetism by Purcell and Morin. Comment (USAPhO/IPhO)

[*] Introduction to Electrodynamics by David J. Griffiths. Comment (USAPhO/IPhO)

[*] Concepts in Thermal Physics by Stephen J. Blundell, Katherine M. Blundell. Comment (USAPhO/IPhO, some chapters are too high level for IPhO)

[*] An Introduction to Mechanics by Kleppner and Kolenkow. (USAPhO/IPhO, some chapters are relevant to F=ma practice). Comment

[*] Vibrations and Waves by A.P French. Comment (USAPhO/IPhO, some chapters are too high level for IPhO)

[*] Thermal Physics by Daniel Schroeder. (USAPhO/IPhO, some chapters are too high level for IPhO) Comment

[*] Modern Physics by Kenneth S. Krane
[/list]
Problem Books/Handouts
[list]
[*] Problems and Solutions in Introductory Mechanics by David Morin (A good book for preparing to the F=ma exam and for practicing basic mechanics)
[*] 200 More Puzzling Physics Problems by Peter Gnadig.
[*] Pathfinder for Olympiad & JEE:Physics by Arwind Tiwari/Sachin Singh. Comment
[*] Problems in General Physics by I.E Irodov.
[*] Jaan Kalda's Handouts by Jaan Kalda (F=ma to IPhO Level Problems) (solutions are found here)
[*] Physics Olympiad - Basic to Advanced Exercises by The Committee Of Japan Physics Olympiad Japan
[*] Competitive Physics: Mechanics and Waves by Wang and Ricardo
[*] Competitive Physics: Thermodynamics, Electromagnetism and Relativity by Wang and Ricardo.
[*] Thinking Physics by Lewis Carroll Epstein (a book of conceptual problems for beginners and intermediate-levels)
[*] 200 Puzzling Physics Problems by Gnadig (USAPhO / IPhO level problems)
[*] Aptitude Test Problems in Physics by S.S Krotov.
[*] 300 Creative Physics Problems with Solutions by Holics (USAPhO / IPhO level problems)
[*] Physics to a Degree by Thomas and Raine (USAPhO / IPhO level problems)
[*] Thinking Like a Physicist by Thompson (USAPhO / IPhO level problems)
[*] F=ma Solutions Manual by Branislav Kisacanin and Eric K. Zhang.
[*] Feynman's Lectures on Physics.
[*] 1000 Solved Physics Problems by Kamal
[/list]

List of Physics Contests
[list]
[*] IPhO Comment
[*] EuPhO Comment
[*] F=ma Exam Comment
[*] USAPhO Comment
[*] Physics Bowl Comment
[*] BAUPC Comment
[*] Pan Pearl River Delta Physics Olympiad Comment
[*] HKPhO
[*] NBPhO
[*] IZhO
[*] Physics Cup Comment
[*] OPhO Comment
[*] Sir Isaac Newton Exam
[*] FYKOS Internet Physics Competition
[*] INPhO
[*] APhO
[*] BPhO
[*] AuPhO
[*] Princeton University Physics Competition
[*] Gulf Physics Olympiad
[*] Online Physics Brawl
[*] PUEC
[*] JPhO (in Japanese)
[*] SwissPhO
[*] Moscow City Physics Olympiad (In Russian)
[*] MIPT (Fiztekh) Physics Olympiad (In Russian)
[*] Saint Petersburg Physics Olympiad (In Russian)
[*] Belarusian Physics Olympiad (In Russian)
[*] EstPhO (in Estonian)
[*] Eötvös Competition (in Hungarian)
[*] Fizika
[*] The University Physics Competition
[*] Rudolf Ortvay Competition in Physics
[*] ThWorldCup
[/list]

Other Resources
[list]
[*] Kevin Zhou's Olympiad Handouts Comment
[*] Physics Olympiad Hub Comment
[*] Everaise Academy Physics Classes Comment
[*] Physics WOOT created by AoPS.
[*] F=ma Problem Series Class created by AoPS.
[*] PhysOlymp
[*] KöMaL Magazine (in Hungarian)
[*] Quantum Magazine.
[*] Physics Genie
[*] Upgrade Your Physics by BPhO.
[*] MIT OCW 8.01 (Classical Mechanics)
[*] MIT OCW 8.02 (Electricity and Magnetism)
[*] MIT OCW 8.03 (Vibrations and Waves/Optics)
[*] AwesomeMath Physics Classes.
[*] Isaac Physics.
[*] Physics Stack Exchange
[*] AoPS Physics Forums :P
[/list]

Summer Camps & Other Opportunities (In progress)
[list]
[*] If you are interested in doing research, consider looking at summer programs offered by your local universities! Many offer one and you can have an internship working with a professor over the entire summer and potentially during the school year as well. If not, cold emailing is also a great option.
[*] Summer Science Program (SSP)
[*] Research Science Institute (RSI)
[*] Quantum School for Young Students (QSYS)
[*] International Summer School for Young Physicists (ISSYP)
[*] Boston University RISE
[*] Summer Program on Applied Rationality and Cognition (SPARC)
[*] High School Honors Science, Math and Engineering Program (HSHP)
[*] University of Florida Student Science Training Program
[*] Texas Tech Clark Scholar Program
[*] Center for Astrophysics, Space Physics & Engineering Research (CASPER)
[*] Yale Summer Program in Astrophysics
[*] MIT Introduction to Technology, Engineering, and Science (MITES)
[*] Garcia Summer Program
[*] George Mason University Aspiring Scientists Summer Internship Program (ASSIP)
[*] Note: I would shy away from "pre-collegiate" summer programs at prestigious universities that have you pay because they are typically a grab for money (6-7k+) and don't really teach you very much (also they admit most students that apply). They don't look that great for a college application either.
[/list]

177 replies

Lol_man000

May 9, 2020

enya_yurself

Aug 13, 2024

J

H

Rotationel Inertia problems for AP Physics FRQ

ehuseyinyigit 2

N Yesterday at 12:31 PM by ehuseyinyigit

Problem 1.
Determine the rotational inertia of a stick with mass $M$ , lenght $L$ with respect to a axis passing from the other side of the stick and perpendicular to it. (Given stick's inertia $1/2ML^2$ ).

2 replies

ehuseyinyigit

Yesterday at 12:26 PM

ehuseyinyigit

Yesterday at 12:31 PM

J

H

Problem from SS Krotov

quasar_lord 6

N Friday at 5:35 PM by whoosh

A small ball moves at a constant velocity $v$ along a horizontal surface and at point $A$ falls into a vertical well of depth $H$ and radius $r$ . The velocity $v$ of the ball forms an angle $\alpha$ with the diameter of the well drawn through point $A$ . Determine the relation between $v$ , $H$ , $r$ , and $\alpha$ for which the ball can "get out" of the well after elastic impacts with the walls. Friction losses should be neglected.

IMAGE

source

6 replies

quasar_lord

Apr 2, 2025

whoosh

Friday at 5:35 PM

J

H

Question Inductors

Riptide1901 10

N Mar 30, 2025 by whoosh

I am confused how the formula $\Delta V=-L\frac{\text{d}I}{\text{d}t}$ aligns with Lenz's law. This implies that as the current is increasing in a certain direction, there is a voltage drop in that same direction. Consider a coil that a wire makes in the $xy$ plane as in the image I attached. If we increase the current, then there is an increasing magnetic field in the $z$ direction. An emf will be produced to oppose this change in current, so the emf will be clockwise (if we are looking at the loop somewhere where $z$ is positive). This implies the voltage decreases when we move clockwise which means voltage decreases when we go leftward ( $z$ direction) instead of rightward. So this implies that there is a voltage drop in the opposite direction that the current is increasing.

10 replies

Riptide1901

Mar 27, 2025

whoosh

Mar 30, 2025

J

H

physics integration

Einstein394 19

N Mar 28, 2025 by whoosh

A chain is held on a frictionless table with length L/4 hanging over. The chain's total length is L. The mass of the chain at a distance x from the end of the chain on the table is equal to bx, where b is a constant. What is the work done to pull the chain fully on the table?

19 replies

Einstein394

Jul 1, 2023

whoosh

Mar 28, 2025

J

H

Kinematics Problem from pathfinder

TensorGuy666 9

N Mar 24, 2025 by Socktuah

3 ants in a table top move in such a way such that they always form vertices of a equilateral triangle whose size is not necessarily constant. If $v_a$ , $v_b$ , $v_c$ denote the speeds of the 3 ants at a particular time, Find the best constant c such that
$\frac{v_c}{v_a+v_b}<=c$

9 replies

TensorGuy666

Jan 29, 2025

Socktuah

Mar 24, 2025

J

H

Terraforming Mars?

cheltstudent 14

N Mar 23, 2025 by cheltstudent

Is it possible?

14 replies

cheltstudent

Mar 21, 2025

cheltstudent

Mar 23, 2025

J

H

Physics "Tricks"

neeyakkid23 4

N Mar 21, 2025 by Riptide1901

Hey guys. I've noticed that there are a decent number of "tricks" in physics problems that can help boost speed and efficiency. An example of which would be:
- One mass colliding with an identical mass at rest will transfer all of its momentum at that angle to it
Is there a list of tricks I should know or are there any other tricks I should know?

4 replies

neeyakkid23

Mar 20, 2025

Riptide1901

Mar 21, 2025

J

H

Relativity

Riptide1901 5

N Mar 20, 2025 by knzhou

There's paradox relating to relativity that I thought of that I cant resolve.

Imagine there is a stick with two rockets at each end that apply an impulse to perpendicular to the end of the stick when fired. In its rest frame, they fire at the same time and the rod does not rotate. But in a frame where the stick is moving, the two rockets firing is not simultaneous so the rod does rotate until the other rocket fires and the rod stops rotating. How is it that the rocket rotates from one perspective and not the other?

5 replies

Riptide1901

Mar 18, 2025

knzhou

Mar 20, 2025

J

H

Fundamentals of physics book for F=MA exam?

MathNerdRabbit103 4

N Mar 20, 2025 by Riptide1901

Hi guys,
Do I need to know calculus to take the F-ma exam? I am only on the intro to algebra book. Also, I want to do good on the USAPHO exam. So can I skip the waves section of HRK?
Thanks

4 replies

MathNerdRabbit103

Mar 18, 2025

Riptide1901

Mar 20, 2025

J

H

STEMS Physics CAT - A OBJ P3

S.Ragnork1729 6

N Mar 20, 2025 by Mathpalkia

Kento had three square-shaped plane mirrors for his experiment. When he looked into one of the mirrors and squeezed his right eye, he saw a reflection as a result. Next, Kento arranged the three mirrors so that they formed three adjacent faces of a cube with a common vertex. The reflecting surfaces of the mirrors were placed on the inner side of the cube. How many reflections does Kento see?

6 replies

S.Ragnork1729

Dec 30, 2024

Mathpalkia

Mar 20, 2025

J