## How to Solve a Multi-Atwood Machine Assembly

Introduction The figure on the right shows a “double-double” Atwood machine with three ideal pulleys and four masses.  All pulleys are released from rest simultaneously.  Which of the choices below describes the angular motion of the top pulley P after some time has elapsed and why? It rotates clockwise with increasing angular speed. It rotates…

## How to Apply Newton’s Second Law to Variable Mass Systems

Introduction The applicability of Newton’s second law in the oft-quoted “general form”  \begin{align}\frac{d\mathbf{P}}{dt}=\mathbf{F}_{\text{ext}}\end{align} was an issue in a recent thread (see post #4) in cases of systems with variable mass.  The following example illustrates the kind of confusion that could arise from the (mis)application of Equation (1): A rocket is hovering in place above ground…

## A Lesson In Teaching Physics: You Can’t Give It Away

A central principle of Physics Forums regarding homework help is not to provide solutions on demand but to guide students along a path to the answer.  The rationale behind this principle is articulated in the familiar saying, “If you give a hungry man a fish, you feed him for a day; if you teach him…

## How to Model a Magnet Falling Through a Conducting Pipe

Introduction In an earlier article, we examined a magnet falling through a solenoid. We argued that the point dipole model can account for the basic features of the induced emf across the solenoid ends. Here, we extend the model to a magnet falling through a conducting pipe along its axis. With the falling dipole moment…

## How to Model a Magnet Falling Through a Solenoid

Introduction Modeling a magnet realistically is a task best done numerically.  Even the simplified model of two separated disks with uniform surface magnetization ##\pm~\sigma_M## involves elliptic integrals simplifying assumptions. As a model, the point dipole may be unrealistic to some but the math is tractable and accessible.  The usefulness of the point dipole model in…

## How to Solve Projectile Motion Problems in One or Two Lines

Introduction We show how one can solve most, if not all, introductory-level projectile motion problems in one or maybe two lines. To this end, we forgo convention.  We demote clock time ##t## to a parameter of secondary importance and ditch the independence of motion in the vertical and horizontal directions. Starting from first principles, we…

## How to Master Projectile Motion Without Quadratics

Introduction In a homework thread a while back a PF member expressed dismay along the lines of “oh no, not another boring projectile motion problem.” Admittedly, I shared the member’s sentiments at the time.  Yet after some thought, I concluded that it is the unvarying recommended strategy of the genre that makes it boring: (a)…

## Why Bother Teaching Mechanical Energy Conservation?

Note: It is assumed that the reader has read part I and part II of the series. Is Mechanical Energy Conservation Free of Ambiguity? Can We Do Better Than Mechanical Energy Conservation? Preface Because of what has already been said, there seem to be three options for proceeding with the teaching of mechanical energy conservation…

## Can We Do Better Than Mechanical Energy Conservation?

Note: It is assumed that the reader has read part I of the series. Introduction The ambiguity and flaws discussed in part I can be resolved using the law of conservation of energy.  In the words of Richard Feynman, There is a fact, or if you wish, a law, governing all natural phenomena that are…

## Is Mechanical Energy Conservation Free of Ambiguity?

Introduction “Close to any question that is in the textbook, there is another question that has never been answered that is interesting.” [Stephen Wolfram, remarks to The University of Vermont physics students, September 30, 2005] Mechanical energy conservation is the assertion that the sum of kinetic and potential energies of a system (the mechanical energy)…

## SOHCAHTOA: Seemingly Simple, Conceivably Complex

What is SOHCAHTOA SOHCAHTOA is a mnemonic acronym used in trigonometry to remember the relationships between the sides and angles of right triangles. Each letter in “SOHCAHTOA” stands for a specific trigonometric function: Sine (sin): The sine of an angle in a right triangle is defined as the ratio of the length of the side…

## How to Zip Through a Rotating Tunnel Without Bumping Into the Walls

Preface While browsing through unanswered posts in the Classical Physics Workshop, I came across a gem at the link shown below.  For the reader’s convenience, I have included (in italics) the OP’s statement of the question. https://www.physicsforums.com/threads/spacecraft-path-with-polar-coordinates.683210/ There is a circular gate rotating at a constant angular speed of  ##\omega##.  The circular gate has a…

## Frames of Reference: Linear Acceleration View

My previous Insight, Frames of Reference: A Skateboarder’s View, explored mechanical energy conservation as seen from an inertial frame moving relative to the “fixed” Earth.  Shifting one’s point of view to the moving frame proved to be somewhat controversial as far as mechanical energy conservation was concerned.  Here I will examine shifting into accelerating frames…

## Frames of Reference: A Skateboarder’s View

My essay Explaining Rolling Motion raised some commentary about frames of reference and their equivalence when solving physics problems. I wish to pursue the idea of shifting one’s frame of reference because its use is relatively uncommon in introductory physics courses.   Students are asked to solve problems mostly in the (approximately) inertial frame of…

## Learn The Basics of Rolling Motion

Although rolling wheels are everywhere, when most people are asked “what is the axis of rotation of a wheel that rolls without slipping?”, they will answer “the axle”.  It is an intuitively obvious answer shared by 3/4 or more of the students in an introductory physics class.  It is also the wrong answer.  Here I…