# Spring 17 Mechanics Week 4

Monday Review for Midterm.

• I noticed that I did not cover stable and unstable equilibrium points in the potential energy graph video, so it may be hard to answer this part of the problem set. At 1:00 Sunday afternoon, I put three questions on the video at 6:45 if you want to watch the video again and fast forward to that point. If the questions don’t appear, you can click at the bottom of the screen to get them to come up again.
• Please read 3.0 friction with three important examples. We didn’t do any friction problems in class, so I encourage you to read this and do the examples because friction is covered in the midterm, and there’s one on the problem set.
• Watch solutions for the last question on PS#3: Throwing Box Off Cliff
• View Big Picture of Mechanics to get an overview of the first 4 weeks of mechanics.
• Solutions for PS#1 sliding down a curved ramp question. I also go over some calculus that may be interesting here. This is from a past class, so the numbers are different.
• This is a slightly different version of the accelerating car, but try this video out if it helps you understand Powerful car accelerating I reference a question from the problem set but this is an old video and I didn’t assign this question this quarter. Thus is is all the more important that you learn from the video.
• If you want more material for midterm #1, I direct you to old exams at the end of week 3 website.

During Class

• My take on how to know which lens you’re to use:
• MOMENTUM: When there is an interaction between two objects, such as a collision, or an “inverse collision” (when one object pushes or pulls on another object). Sometimes you consider both bodies, but sometimes you just consider one, like when the earth pulls on your body, and we really don’t consider what happens to the motion of the earth.
• ENERGY: When there is a before and after that converts energy. Things like height and speed have a corresponding energy terms like PE and KE.
• DYNAMICS: if there are forces and acceleration.
• KINEMATICS: when everything in front of you has to do with displacement and the time rates of change. In particular, you already have these equations, and don’t have to figure them out by examining forces, momentum, or energy.
• as we examined in class, some interactions require more than one lens – such as which curved frictionless track brought the ball to the end in the shortest amount of time. We need to consider energy (or dynamics) to compare their speeds, and then kinematics to compare times from speeds.… or most obviously, the ballistics pendulum, which requires energy and momentum.

Questions about midterm:
– The midterm covers everything we’ve talked about in class, saw in videos, or had in assigned readings (including friction). In short, if you’ve been exposed to it though the class, then please expect that it could be covered on the exam.

What about “smart” calculators? You are not allowed to use calculators that graph or can integrate or take derivatives or anything like that… My strong preference is that you use no calculator whatsoever and just estimate… you can write “no calculator” on your exam and I will like it! However, if you feel better about having a calculator, I understand. If you do use a calculator, please find a simple calculator with only trig, square roots and simple math. – Thanks

Tuesday Midterm #1

Wednesday

PS#4 is due next Monday and the first part is complete corrections for MT#1.

This week, we will almost identically repeat what we’ve done the first 4 weeks, but this time for rotational motion.

All the concepts are the same, so taking three weeks, should work well. Your learning objective is to recognize the analogies between the linear concepts and the rotational concepts. Then you should identify the formulas central to each and consider how they are going to be used in similar ways.

We will start mixing chapters from OpenStax when I find them appropriate. This will be longer and more technical than my short text notes. I may also write some more chapters, but it is less necessary now that we have finished linear mechanics. It wasn’t appropriate for us to use a standard text before because of the way we introduced all the concepts at once. However, now some of the chapters are appropriate for us because we’ve finished linear motion.

Before Class

• See 4 Lenses of Rotational Motion Oh my, this video is way way too long. Please watch it in two sittings and take notes.
• Please read my short short introduction to rotation: 4.0 Introduction to Rotation
• Please read through the OpenStax 10.1 Intro Chapter on Rotations They introduce cross product here, which is great, but we won’t make too big of a deal out of it. HOWEVER, please pay particular attention to the right hand rule in determining direction of rotation (fig. 4). This is something I don’t cover in class and it is crucially important.
• PS#4 begins with redoing MT#1. Please start on that. I have posted MT#1 on the main class website.

During Class

Thursday

Know how to calculate Torque

In a statics problem where alpha = 0, can you set the sum of the torques = zero (like you did with forces for linear motion)

Before Class

• Please See Video: which includes the fundamentals of rotational dynamics and rotational kinetics.
• Please read OpenStax 10.4 Moment of Inertia and Rotational Kinetic Energy. This is largely a review of the moment of inertia video. Please look it over and see that it makes sense. Additionally please spend some time on Fig. 4, which I don’t provide any where else, and make sure you can answer the question of why the coefficients are bigger or smaller than others.
• Please read OpenStax 10.5 Moment of inertia of a solid body through integrating over the entire body. This chapter covers the parallel axis theorem, which we won’t do it until later in the quarter.

In Class

Working out with the “inertia wand”

After Class

I added MT#1 comments to the main class website. This provides some direction.