# AT Cycle 9

## 10/24 - 10/29

Th 10/24

F 10/25

M 10/28

T 10/29

### 🔴 2: Th 10/24, 🟡 4: Th 10/24, 🔵 8: Th 10/24 - center of mass problems (1)

Daily Check-in: center of mass summation (a similar example if you missed class)

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

Some of these problems will require you to use the calculus and what you learned about different kinds of densities. If you finish the ones that don't require calculus, watch the homework videos below.

Homework: Quiz on center of mass, rotational kinematics, and tipping - Wednesday, October 30th. Watch the following two videos about how to find the center of mass of an extended object with calculus. Also, make sure that you're comfortable with Example 9-14 on page 223 of the Giancoli textbook.

### 🟥 2: M 10/28 lab, 🟨 4: F 10/25 lab, 🟦 8: F 10/25 lab - CoM (2) & rotational kinematics

Daily Check-in (hour 1): center of mass integral

Today, we'll collaboratively finish solving 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

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

Then during the second hour, 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.)

Fill out the handout first which will relate Translational & Rotational Kinematics Variables using what you learned in the video. 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

Homework: Quiz on center of mass, rotational kinematics, and tipping - Wednesday, October 30th. Complete the required center of mass problems above. 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 λ = kx3. Then, answer the following questions in a ✏️ Google Classroom assignment by Monday, October 28th 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:

### ❤️ 2: T 10/29, 💛 4: M 10/28, 💙 8: M 10/28 - moment of inertia

Daily Check-in: translational vs. rotational variables

Today, we'll start by learning first 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. Demos: two different rods with the same mass but different moments of inertia; ring and solid disk rolling down ramp.

Homework: Quiz on center of mass, rotational kinematics, and tipping next class - Wednesday, October 30th. If you have any questions about the lecture today, you may watch my video lecture, and make sure you watch the part about parallel axis theorem starting at minute 33.