# AT Cycle 9

## 10/27 - 11/1

W 10/27

Th 10/28

F 10/29

M 11/1

### π΄ 1: W 10/27, π‘ 3: W 10/27 - 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.

Center of mass example with calculus:

### π₯ 1: F 10/29 lab, π¨ 3: Th 10/28 lab - center of mass problems

Daily Check-in: center of mass summation/integral

Today, we'll collaboratively solve center of mass problems from Chapter 9:

Support: 2, 4
Required: Sample prob 9.02, 5, 7, 8, 15, 16, 17, 114, G65
Enrichment: 14, G66, G67

These problems will require you to use the calculus and what you learned about different kinds of densities.

Homework: Finish all required problems you did not get to in class. It is very important that you do these required problems. Also, make sure that you're comfortable with Example 9-14 on page 223 of your textbook. Try recreate the solution the problem from the 3rd and 4th video from last night independently. That means to write out your own solution without watching the video. The problem is to find the center of mass of a non-uniform rod length L where Ξ» = kx3. Then, answer the following questions in a βοΈ Google Classroom assignment by Friday at 10pm.

• How do you know that you need an integral to solve this problem?

• What general formula do you need to use?

• Why do you need to change the formula to dx?

• How do you change the formula to dx?

• How do you know which variable determines the limits?

• How do you know where x = 0? (kind of a trick question)

• How do I know the units of my solution are correct?

If you get stuck, rewatch the videos:

And if you need a review of the center of mass integral that we did in class, watch my video:

### β€οΈ 1: M 11/2, π 3: F 10/29 - moment of inertia

Today, we'll spend the period first learning about what moment of inertia is and then trying to figure out how to calculate the moment of inertia of different objects. We'll learn formulas for moment of inertia using a summation for discrete objects and then an integral for continuous bodies. With any time remaining, start problems from the next post.

Homework: If you have any questions about the lecture today, you may watch my video lecture: