Mechanics

Velocity Time Function

Revisiting the Velocity-Time Function

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Kinematics: The Velocity-Time FunctionAuthor's Preface: A Collaborative Approach to Lesson Development The intention behind what I hope will be…
no tidal bulge

Why the Tidal Bulge Doesn’t Exist – Tidal Theory Explained

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9 Comments
Introduction Overview That there is no tidal bulge is the key premise of this article. Upper-level oceanography undergraduates and above know this. Yet…
slinky drop experiment

The Slinky Drop Experiment Analysed

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The slinky drop is a rather simple experiment. In its most basic form, it requires only a popular toy for children, a stable hand, and a keen eye.…
Multi-Atwood Machine Assembly

How to Solve a Multi-Atwood Machine Assembly

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IntroductionThe figure on the right shows a "double-double" Atwood machine with three ideal pulleys and four masses.  All pulleys are released from…
Variable Mass Systems

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

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Introduction The applicability of Newton's second law in the oft-quoted "general form"  $$\begin{align}\frac{d\mathbf{P}}{dt}=\mathbf{F}_{\text{ext}}\end{align}$$…
object slide down ramp physics

Subtleties Overlooked in Friction Questions: Object Slides Down Ramp

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Problem statement (simplified) An object slides down a ramp at angle θ to encounter level ground. Both surfaces have kinetic friction: μ' on the ramp,…
why can we jump

How Can We Jump When the Ground Does No Work?

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Common mistaken argument It is relatively common on Physics Forums to see arguments that are effectively similar to the following: When we jump off the…
MIT course corrections

Corrections to MIT Open Courseware: Systems of Varying Mass

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Corrections to MIT Open Courseware 8-01sc classical mechanics, fall 2016 Applying Newton's Laws to systems of Varying Mass PDF Course Link My concerns…
Quaternions in Projectile Motion

Quaternions in Projectile Motion

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Introduction In a previous Physics Forums article entitled “How to Master Projectile Motion Without Quadratics”, PF user @kuruman brought to our…
safety

Safety Factors: Why Forums Avoid Design Advice Online

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7 Comments
Forum Guidelines There are often questions on Physics Forums related to building machines or structures that are left unanswered because of this guideline…
solving projectile motion

How to Solve Projectile Motion Problems in One or Two Lines

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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…
physics cannonball projectile

Maximizing Horizontal Range of a Projectile

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Introduction A recent homework problem that appeared in the forums was concerned with maximizing the horizontal range of a projectile subject to the launch…
equations of motion

Equations of Motion Revisited

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Introduction In any school Physics course, the Newtonian equations of motion are very much a 'stock' item. Students learn the equations and are given…
projectile motion

How to Master Projectile Motion Without Quadratics

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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."…
strings waves

Intro to Physically Reasonable Waves on a String

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Introduction Physics teachers who are either writing physics questions that deal with waves on a string or setting up equipment for a class lab or demo…
energy conservation can we do better

Can We Do Better Than Mechanical Energy Conservation?

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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…
elastic ball collision

An Alternate Approach to Solving 2-Dimensional Elastic Collisions

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Introduction This article follows on from the previous on an alternate approach to solving collision problems. In that article, we determined the equal…
energy conservation ambiguity

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,…
Collision problems

An Alternative Approach to Solving Collision Problems

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Introduction Collisions are very much a stock item in any school physics curriculum and students are generally taught about the use of the principles…
Learn Dimensional Analysis

Learn the Basics of Dimensional Analysis

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As a university teacher and as a PF member, I have often noted that students are largely unaware of or not using dimensional analysis to help them in their…
rotating room

How to Transit a Rotating Tunnel: Physics & Trajectories

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Introduction Preface While browsing through unanswered posts in the Classical Physics Workshop, I came across a gem at the link shown below. For the…
What is potential energy

Potential Energy Explained — Definitions & Formulas

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Definition / Summary Potential energy is the negative of the work done by a conservative force. It represents stored mechanical energy associated with…
Moment of Inertia

Moment of Inertia: Definitions, Formulas & Tensor Guide

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Definition / Summary The moment of inertia is a property of a rigid body that relates torque (rotational force) to rotational acceleration in the same…
Maupertuis Principle

A Pure Hamiltonian Proof of the Maupertuis Principle

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Here is another version of proof of Maupertuis's principle. This version is pure Hamiltonian and independent of the Lagrangian approach.The proof…
Simple Harmonic Oscillator Laboratory

An Accurate Simple Harmonic Oscillator Laboratory

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[CONTENT] Learning ObjectivesExecute a specific experimental procedure to test a specific hypothesis. Use the Tracker video analysis software for…
Hooke's Law Experiement

An Example of An Accurate Hooke’s Law Laboratory

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16 Comments
Learning Objectives Gain confidence and experimental care in making accurate measurements. Understand the relationship between force and spring…
vehicle power

Why Power Determines Vehicle Acceleration Limits

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33 Comments
Introduction One interesting problem when dealing with a vehicle of a certain mass is to determine what is required to get the maximum acceleration while…
rotational mechanics

An Example of Servo-Constraints in Mechanics

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Servo-constraint was invented by Henri Beghin in his Ph.D. thesis in 1922. For details see the celebrated monograph in rational mechanics by Paul Appell.To…
speed of sound

Direct Echo-Based Measurement of the Speed of Sound

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42 Comments
Figure 1: Distance vs. time a firecracker report echoed off of a building at different distances on both a cold and a warm day.Introduction The…
EdmondHamilton

The Second Satellite: Orbit, Gravity & Tidal Errors

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Introduction This article won't contain much about physics that typical readers of this site don't already know. However, deconstructing improper physics…
dampedforces

Learn Damped Motion in Classical and Quantum Mechanics

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This Insights article is about dissipative forces (friction, air resistance, viscosity...).Damping by friction forces is one of the concepts that is…
linearacceleration

Frames of Reference: Linear Acceleration View

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My previous Insight, Frames of Reference: A Skateboarder's View, explored mechanical energy conservation as seen from an inertial frame moving relative…
angledimensions

Can Angles be Assigned a Dimension?

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1. Some Background on Dimensional Analysis ... if you are not already familiar with it. 1.1 Dimensions Dimensional Analysis is a way of analyzing…
frameofreference2

Frames of Reference: A Skateboarder’s View

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My essay Explaining Rolling Motion raised some commentary about frames of reference and their equivalence when solving physics problems. I wish to pursue…
rollingmotion

Learn The Basics of Rolling Motion

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50 Comments
Introduction Although rolling wheels are everywhere, when most people are asked "what is the axis of rotation of a wheel that rolls without slipping?",…
acusticbeats

Mathematics of Acoustic Beats: Explanation & Examples

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Introduction Purpose and scope In late high school physics courses and first-year university courses, the phenomenon of acoustical 'beats' (digital audio)…
Brachistochrone

Explaining the General Brachistochrone Problem

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Consider a problem about the curve of fastest descent in the following generalized statement. Suppose that we have a Lagrangian system $$L(x,\dot x)=\frac{1}{2}g_{ij}(x)\dot…
basickinematics

Learn Basic Kinematics in Classical Mechanics

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There is an interesting thing in teaching of Classical Mechanics. Several theorems which presented below form a core part of kinematics for all Russian…
kinematics

Presenting a Rare Kinematic Formula

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Here we present some useful kinematic fact which is uncommon for textbooks in mechanics. Consider a convex rigid body (RB) rolling without slipping…
angularvelocity

Elementary Construction of the Angular Velocity

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Physics books seldom contain an accurate definitions of the angular velocity of a rigid body. I believe that the following construction is as simple as…
physics_vectors

Frequently Made Errors in Vectors – Elementary Use

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 A vector has magnitude and direction. Pictorially, a vector can be imagined as a location in n-dimensional space relative to some fixed origin. …
secondaryforces

Introduction to the Secondary Forces in Physics

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Many are familiar with the "fundamental forces" of nature: gravity, electromagnetism, and the strong and weak nuclear forces. Three of these tend to bind…
earthgravity

Learn All About Earth’s Gravity

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Introduction Earth's gravitational field at the surface is approximately 9.8 Newtons/kilogram or 9.8 meters/second/second. But how does that change due…
gravityacceleration

Why Is Acceleration Due to Gravity a Constant?

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This question has popped up many times. So here is an attempt to address it.To answer this question at the elementary level, several assumptions will…
What is Energy

A Definition and Controversy of Energy

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[CONTENT] What is energy? Energy is a fundamental concept that refers to the capacity of a system to do work. It is a scalar quantity, meaning it has magnitude…
Coriolis

Frequently Made Errors: Pseudo and Resultant Forces

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  1. Real versus Fictitious Pseudo, or "fictitious", forces can arise when a non-inertial frame of reference is used. Using a non-inertial frame…
errors springs

Frequently Made Errors in Mechanics: Springs

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  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…
impact errors

Frequently Made Errors in Mechanics: Momentum and Impacts

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  An impact is an impulse (change of momentum) that involves arbitrarily large forces acting very briefly. These result in near-instantaneous…
subway

Brachistochrone Subway Tunnels: Speed vs. Depth Tradeoffs

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Introduction A subway tunnel could, in principle, operate without external energy (like electricity) if we assume zero friction everywhere. The train would…
kinematic errors

Frequently Made Errors: Kinematics Mistakes Explained

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Kinematics is the subset of dynamics that only concerns itself with time, displacement, velocity, and acceleration. A problem is a kinematics problem…
mistakes moments

Frequently Made Errors: Mechanics — Moments and Torque

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Entire List for Frequently Made Errors Series MechanicsForces Friction Moments Kinematics Hydrostatics Momentum and Impacts Springs Pseudo…
friction

Frequently Made Errors in Mechanics: Friction

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1. Direction of the normalDefinition: The normal force that body A exerts on body B is that force of minimum magnitude which suffices to prevent penetration…
forces mistakes

Frequently Made Errors in Mechanics: Forces

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Entire List for Frequently Made Errors Series Mechanics Forces Friction Moments Kinematics Hydrostatics Momentum and Impacts …
hand_to_hand_combat

Hand-to-Hand Combat Physics — Force, Momentum, Speed

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Physics of Hand-to-Hand Combat Hand-to-hand combat (often abbreviated H2H or HTH) refers to fighting at very close range, usually without weapons. It includes…