Fall 2016 Mechanics Week 5

We took MT#1 last Thursday. PS#4 is due this coming Thursday and the first part is complete corrections for MT#1.

For Tuesday,
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.

First Hour

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. There are two reasons that I have waited until now to do this: (1) I just became aware that the text is available. They’ve been planning it for two years now. (2) It wasn’t appropriate for us 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
  • See Circular Motion, Introduction
  • 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 has been posted on main class website. Please give it a read immediately so you know what we are getting ready to do. It is due on THURSDAY already!

During Class

Second Hour
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

In Class

After Class

Thursday: Angular Dynamics and Statics.
First Hour
Master the use dynamics (vector sum of the torques = I * alpha) just as you did for force and acceleration in linear motion
Augment your use of Work-Energy Theorem with rotational kinetic energy.

Before Class:

In Class
Collect PS#4
Collect Improved Project Report

After Class

Second Hour
Conserving Angular Momentum, when Sum of the Torque = zero

  • Angular momentum = I*alpha, kind of like linear momentum = m*v
  • Torque SOMETIMES = I * alpha, as stated above in rotational dynamics. Torque ALWAYS = rate of change of angular momentum
  • For instance if Torque = zero, then angular momentum is conserved (just like we conserve momentum if there’s no outside force) it doesn’t mean that alpha = zero, like acceleration = 0 if the sum of the forces = 0, Think of the spinning skater pulling in her arms, yielding a positive angular acceleration.

Before Class

  • Please watch this video on torque = time derivative of angular momentum
  • Please read 4.6 Introduction to Angular Momentum.
  • There’s only one physics video, so I want you to be aware of one more thing: just like F=ma, for rotational problems we use Torque = I*alpha. Please identify in your problem set which questions involve this Rotational Dynamics. Then, please describe a protocol for rotational dynamics (Forces) that is a rotational analogue of our protocol for linear dynamics.

In Class:
Dropping kids on merry-go-round

After Class