# AT Cycle 9

## 10/26 - 10/31

**W 10/26**

**Th 10/27**

**F 10/28**

**M 10/31**

### π΄ 2: Th 10/27a, π‘ 4: W 10/26 - integrals intro

Today, for those who haven't completed a calculus course yet, we'll talk about the **basics of derivatives and integrals, and see how this would help us with kinematics problems**. You'll be grouped heterogeneously in small groups to learn about what derivatives and integrals are. We'll look particularly at velocity vs. time graphs.

**Homework**: If you're new to integrals, review the Introduction to Calculus Presentation. Write down any questions you have, and be sure to ask your group next class. Also, try to get ahead on video watching. This is a busy week with a lot of videos to watch. With Halloween coming up, it'd be best if you are working ahead slightly.

### π₯ 2: Th 10/27b, π¨ 4: Th 10/27 - kinematics with calculus

Today, we'll continue our discussion of calculus in the context of kinematics. For those students who have already taken calculus, you'll be working the following Chapter 2 problems and non-uniform acceleration worksheet. (The answer to #1 is incorrect on the website; it should be 1/3 m.)

For those who have already completed one year of calculus and beyond:

Required: Ch 2 #17, 22, 81, 82, 86, Worksheet #1-3 ****

Enrichment: Worksheet #4 and AP problem on back - 2010M3, #104, 119

For those taking calculus for the first time this year:

Required: Ch 2 #15, 16, 17, 22, 81, 82, Worksheet #1-2

Enrichment: Ch 2 #86

**** There's an error in the answer for Worksheet #1 - it should be 1/3.

**Homework**: The above problems on kinematics with calculus are due to βοΈ Google Classroom by Friday, October 28th at 10pm. If you have issues understanding how calculus applies to kinematics, rewatch some videos from the past week or read the textbook Chapter 2. Make sure you've done required problems at least. Watch the video below on **rotational kinematic variables**. Take notes while you watch! Understanding these concepts are EXTREMELY IMPORTANT in being successful in the rest of this unit, so take the time to rewind and rewatch as needed. (When Mr. Fullerton derives centripetal acceleration in minute 13, he talks about unit vectors. "I-hat" is a unit vector magnitude 1 in the x direction. "J-hat" is a unit vector magnitude 1 in the y direction. Unit vectors are really just multipliers which turn scalar magnitudes into vectors with direction.)

**Weekend Homework**: Get ahead on videos on the rest of this page, especially if you have Halloween plans!

### β€οΈ 2: F 10/28, π 4: M 10/31a - rotational kinematics

*Daily Check-in: translational vs. rotational variables*

Today, fill out the handout first which will relate Translational & Rotational Kinematics Variables. Then, we'll do problems from Chapter 10 which will allow you to practice **applying the rotational kinematics formulas**.

Support: 3, 4, 10

Required: 6, 7, 14, 16, 22, 26, 28, 32

Enrichment: 8, 17, 31

Use the notes you took on the video you saw last night. If you finish early, start watching the many videos for tonight's homework.

**Homework**: The above problems are due in βοΈ Google Classroom by Wednesday, November 2nd at 10pm. Watch the following videos on center of mass. Although there are quite a few videos, each one is not very long.

If you can get ahead on homework videos from the next post, that'd be great. Watch the first two videos below. We'll need this information by Tuesday, and there are 4 longer videos to watch Monday night. If you have Halloween plans, you may want to watch all 4 of the videos from the next post over the weekend. They are very important!!!

### π 2: M 10/31, π 4: M 10/31b - density lab

Today, we'll** review what you know about density and introduce the concepts of linear and surface densities**. We'll perform a lab together that requires you to measure, estimate, and find other information. Write up your lab, and hand it in next class.

If you finish early, then start watching the videos below on center of mass.

**Homework**: Watch the following videos on finding the center of mass of an object. The first video shows you the theory on finding the center of mass. The second video shows you how to find the center of mass of an object using the summation. The third and fourth videos show you how to use the integral to find the center of mass. Sorry for the long homework.

**Period 2 - Watch all four videos by Wednesday's class.Period 4 - Watch the first two videos by Tuesday's class, and watch the 3rd and 4th videos by Wednesday's class.**

Center of mass example with calculus: