In this video David quickly reviews the momentum and impulse topics on the AP Physics 1 exam and solves an example problem for each concept. Created by David SantoPietro.

Investigate collisions on an air hockey table. Set up your own experiments: vary the number of discs, masses and initial conditions. Is momentum conserved? Is kinetic energy conserved? Vary the elasticity and see what happens.

16.225 is a graduate level course on Computational Mechanics of Materials. The primary focus of this course is on the teaching of state-of-the-art numerical methods for the analysis of the nonlinear continuum response of materials. The range of material behavior considered in this course will include: linear and finite deformation elasticity, inelasticity and dynamics. Numerical formulation and algorithms will include: Variational formulation and variational constitutive updates, finite element discretization, error estimation, constrained problems, time integration algorithms and convergence analysis. There will be a strong emphasis on the (parallel) computer implementation of algorithms in programming assignments. At the beginning of the course, the students will be given the source of a base code with all the elements of a finite element program which constitute overhead and do not contribute to the learning objectives of this course (assembly and equation-solving methods, etc.). Each assignment will consist of formulating and implementing on this basic platform, the increasingly complex algorithms resulting from the theory given in class, as well as in using the code to numerically solve specific problems. The application to real engineering applications and problems in engineering science will be stressed throughout.

An interesting case of price elasticity of demand is a demand curve with a constant unit elasticity. Explore what such a demand curve would look like in this video. Created by Sal Khan.

Price of one good impacting quantity demanded of another. Created by Sal Khan.

Walk through the logic of determining what kind of good has the most elastic demand in this video.

There are several factors that affect how elastic (or inelastic) the price elasticity of demand is, such as the availability of substitutes, the timeframe, the share of income, whether a good is a luxury vs. a necessity, and how narrowly the market is defined. We explore each of these in this video.

Why we calculate percent changes in a strange way when calculating elasticities. Created by Sal Khan.

This subject provides an introduction to the mechanics of materials and structures. You will be introduced to and become familiar with all relevant physical properties and fundamental laws governing the behavior of materials and structures and you will learn how to solve a variety of problems of interest to civil and environmental engineers. While there will be a chance for you to put your mathematical skills obtained in 18.01, 18.02, and eventually 18.03 to use in this subject, the emphasis is on the physical understanding of why a material or structure behaves the way it does in the engineering design of materials and structures.

Elasticities can be calculated for more than just price elasticity of supply or price elasticity of demand. For example, income elasticity of demand as a measure of how quantity demanded changes in response to income.

Economists use the concept of price elasticity of demand to describe how the quantity demanded changes in response to a price change. In this video, explore a simple way to calculate the price elasticity of demand, how to interpret that calculation, and how price elasticity of demand varies along a demand curve.

We can calculate the price elasticity of supply to gauge how sensitive percent changes in quantity supplied are to percent changes in price.

" Here we will learn about the mechanical behavior of structures and materials, from the continuum description of properties to the atomistic and molecular mechanisms that confer those properties to all materials. We will cover elastic and plastic deformation, creep, fracture and fatigue of materials including crystalline and amorphous metals, semiconductors, ceramics, and (bio)polymers, and will focus on the design and processing of materials from the atomic to the macroscale to achieve desired mechanical behavior. We will cover special topics in mechanical behavior for material systems of your choice, with reference to current research and publications."

Introduction to statics and the mechanics of deformable solids. Emphasis on the three basic principles of equilibrium, geometric compatibility, and material behavior. Stress and its relation to force and moment; strain and its relation to displacement; linear elasticity with thermal expansion. Failure modes. Application to simple engineering structures such as rods, shafts, beams, and trusses. Application to design. Introduction to material selection. This course provides an introduction to the mechanics of solids with applications to science and engineering. We emphasize the three essential features of all mechanics analyses, namely: (a) the geometry of the motion and/or deformation of the structure, and conditions of geometric fit, (b) the forces on and within structures and assemblages; and (c) the physical aspects of the structural system (including material properties) which quantify relations between the forces and motions/deformation.

Looking a bit deeper at why elasticity changes despite having a linear demand curve. Created by Sal Khan.

In this video, take a deeper dive into the total revenue rule and the relationship between total revenue and elasticity. Created by Sal Khan.

Examining the two extremes of elasticity, perfectly elastic and perfectly inelastic demand, can help us beter understand the intuition behind this measure. Created by Sal Khan.