Entries by kuruman

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

Preface My first experience with derivatives was seeing how they are obtained from the usual definition $$f'(x)=\underset{\text{$\Delta $x}\to 0}{\text{Lim}}\frac{f (\text{$x+\Delta $x})-f (x)}{\text{$\Delta $x}}.$$ I accepted the binomial theorem derivation in the case of polynomials and the small angle explanation in the case of sines and cosines  until my math instructor asserted, without justification, that the…

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…

Explaining How Rolling Motion Works

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…