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Energy Summary The article addresses the fundamental question, “What is energy?” and explores why discussions about energy can be challenging. It introduces the Newtonian mechanics definition of energy, which defines energy as the capacity of a system to do work and work as a force applied over a distance. The concept of kinetic energy, derived…
We are still discussing the final year of your undergraduate education. So far, we have covered what you need to consider if you want to go on to graduate school and prepare yourself as best as you can for that part of your journey. This is the “traditional” path that many physics students…
1. Real versus Fictitious Pseudo, or “fictitious“, forces can arise when a non-inertial frame of reference is used. Using a non-inertial frame makes the usual force/acceleration laws fail. Pseudo forces must be added to correct them. 2. Applied versus Resultant The applied forces on an object are the specific forces exerted on it by…
Introduction This is a follow on from my paper explaining renormalization. A question was raised – why exactly do we need a cut-off. There is a deep reason to do with dimensional analysis, and the power series expansion used in perturbation theory. Along the way, we will see renormalization in a more general setting, and…
1. Springs in Series “A spring of constant ##k_1## is connected in series with a spring of constant ##k_2##. What is the spring constant for the composite spring?” Attempted answer: When the tension in the first spring is T, the tension in the second spring will also be T. The two extensions will be…
An impact is an impulse (change of momentum) that involves arbitrarily large forces acting very briefly. These result in near-instantaneous changes in speed. In general, work will not be conserved. 1. Examples of impacts Most textbook impacts are collisions, but anything involving a sudden change in speed is an impact. For example, a…
1. Archimedes’ Principle X “When a body is placed in a liquid, the weight of the body equals the weight of the liquid displaced” That will only be true if the body is floating. Here’s what Archimedes wrote: ✓ “Any object, wholly or partially immersed in a fluid, is buoyed up by a force…
1. Algebra versus Arithmetic When numerical values are provided as inputs in a question, it is tempting to plug these into the equations straight away. Resist! Create variable names for these constants and work wholly symbolically until the final step. There are many advantages: If you make a mistake, it takes less time to…
Kinematics is the subset of dynamics that only concerns itself with time, displacement, velocity, and acceleration. A problem is a kinematics problem if it involves those quantities, but consideration of masses, forces, and work are unnecessary. 1. Scalars and Vectors X “A scalar only has magnitude while a vector has magnitude and direction”…
The term “moment” is used in various ways in Physics and Mathematics: Given a force and a reference point, the force has a moment (or torque) about the point. A rigid body has moments of mass of various orders (zeroth, first, second..) Similarly, moments of area, and moments of statistical distributions This page only…
What Is The Issue With Renormalisation If you have an interest in physics you have likely come across renormalisation before, although what it really is would probably have not been explained. Instead, you would read Dirac never accepted it, Feynman called it a ‘dippy process’, and if you look under a quantum theorists rug you…
1. Direction of the normal Definition: The normal force that body A exerts on body B is that force of minimum magnitude which suffices to prevent penetration of its surface. X “the normal is at right angles to the horizontal” This mistake tends to arise when one of the bodies presents a sharp corner…
Introduction There are many sins in physics didactics. Usually, they occur, because teachers, professors, textbook or popular-science-book writers, etc. try to simplify things more than possible without introducing errors in reasoning, or they copy old-fashioned methods of explaining an issue, leading to the necessity to “erase” from the students’ heads what was hammered in in…
Notation: On this page, a circumflex signifies an average. 1. Forces as vectors A force is a vector, i.e. has magnitude and direction. But it also has a point of application, which vectors, in general, do not have. A force can be thought of as a vector pair, one vector specifying its magnitude and…
Introduction The particle in a box is a staple of entry-level Quantum Mechanics classes because it provides a meaningful contrast between classical and quantum dynamics. It is one of the few problems that can be solved exactly, without approximations. Despite this, I would wager that most of you solved only the 1-D particle in a…
Introduction The second law of thermodynamics and the associated concept of entropy have been sources of confusion for thermodynamics students for centuries. The objective of the present development is to clear up much of this confusion. We begin by first briefly reviewing the first law of thermodynamics, to introduce in a precise way the concepts…
Albert Einstein is arguably the most famous scientist of all time, but how much do you actually know about him? Let’s find out by taking this quiz! No prizes, so no Googling. (post your honest score in the discussion thread) Ready for your next quiz? How well do you know Isaac Newton? 1. Who…
*This Insight is intended to have a logical basis but not to be taken as purely factual or legal advice. Key Points Outer Space Treaty does not provide clear guidance on the legality of satellite–based lasers One should apply to the ITU when planning a telecommunication satellite Do not interfere with remote sensing activities of other…
Bioethics Key Points Worrying about the future now means recognizing the advances in technology, such as genetic engineering, that have arisen. There is a standard of health that fluctuates depending on relative perceptions of different biological variations on the human species that may emerge. We must be careful when using new technologies and understand their…
Discussing science online can often be a frustrating experience if no quality controls are in place, which is often the case. As part useful reference and part entertainment PF has put together an adequate list of common attributes associated with dubious scientific discussion. Next time you’re in a discussion, check this list to see if…
Hand-to-Hand Combat Key Points Martial arts effectively use principles of physics to achieve goals quickly and forcefully. Athletic intelligence enables humans to quickly adapt to the physical laws of nature. The most successful styles used by military forces rely heavily on physics. Acceleration, force, momentum, and energy are all integral aspects of martial arts. Jiu–Jitsu…
Meet a Mentor is a biweekly (twice a week) series to help you get to know your wonderful Mentors better. Constructive questions and comments are welcome! Today we meet: Integral Can you give us a brief bio? I am a 2nd generation Oregonian born smack in the middle of the 20th century. My dad came to…
Meet a Mentor is a fun series to help you get to know your wonderful Mentors better. Constructive questions and comments are welcome! Today we meet: @Ryan_m_b Give us a brief history of Ryan_m_b I’m in my mid-twenties, spent most of my life living in a small town on the border of the country side but…
Meet a Mentor is a series to help you get to know your wonderful Mentors better. Constructive questions and comments are welcome! Today we meet: Mark44 How did you become interested in mathematics? Along about 4th grade I came across an algebra textbook that really fascinated me, with all of its x’s and y’s, and symbols…
Key Points Evolution is a theory, which is the foundation of science 2. Evolution is the most rational explanation for the existence of life Creationism stems from denial and dogma, not evidence Intelligent Design is an attempt to shoehorn a God into the theory of evolution Evolution does not necessarily clash with religion The second…