We are in the second half of the quarter and time is flying by. Hopefully you feel more comfortable managing your time for this class around your other obligations and appreciate the consistent cadence of our learning activities.

This week we will explore the universal law of gravitation and other central forces that keep objects accelerating centripetally. We will also reflect on our empathy self-intervention and expand our awareness of how our actions affect others.

Learning Outcomes

By the end of this week you will be able to:

Apply conservation of angular momentum to systems of masses with and without external torques
Explain how central forces result in centripetal acceleration
Identify forces acting to keep a body accelerating centripetally
Describe what the inverse square law means in various contexts
Apply the universal law of gravitation to bodies in low earth orbit
Explain how centripetal acceleration affects motion in a loop-the-loop

Day 21 | Monday 2/7 | Torque and Angular Momentum

Today is about emphasizing the crucial role played by angular momentum conservation. Say it!: "Torques change angular momentum." In the video on the Big Picture of Rotation, you will notice two references to precession (that we haven't covered yet) from 5:11 - 6:00 and and from 9:08 - 9:24. You may find this interesting, but you are not responsible for it until Week 8/9. We'll revisit this video at the end of the quarter, but it's also a very good review right now.

Goals:

By the end of today you will be able to...

Identify how torques change angular momentum
Apply angular momentum conservation to systems with changing moment of inertia
Describe how the lenses of rotational motion fit in to the big picture of mechanics
Explain how a Pelton Wheel Turbine works

Before Class:

Assignment: Please submit your Empathy Self-Intervention
Video: Watch Torque = Angular Momentum Rate of Change [4m10s]
Video: Watch Rotational Mechanics Big Picture [11m19s]
Textbook: Read Ch 4.7 - Introduction to Angular Momentum Conservation [2 pg, 2 ex]
Textbook: Read Ch 4.8 - Update on Lens Method Including Rotation [1.5 pg, 0 ex]
Discussion: Please leave a statement or question on our Week 6 Reading Discussion
Video: Watch Pelton Wheel, Turbine [2m51s]
Survey: Take this Short Survey - Day 21 [2 questions]
Reflect: Consider the question we ended with Thursday: which wheel (ring or disk) reaches a higher position on the ramp?

During Class:

We will discuss the wheel demo and observe the results
We will consider how angular momentum is conserved when moment of inertia changes
We will consider a cart and a wheel rolling down a ramp
We will review our Short Survey results

Day 22 | Tuesday 2/8 | Centripetal Acceleration

When objects move in a circle at constant speed, they are always experiencing a force. How do we know? Velocity is a vector. Vectors have both magnitude and direction. If direction is changing, velocity is changing. What force is causing the change? There are some common misconceptions out there (you might have learned them in a prior physics class!) and at's what we need to talk about...

Goals:

By the end of today you will be able to...

Explain what a central force is and how it causes centripetal acceleration
Identify the forces causing a centripetal acceleration
Solve for centripetal acceleration and the forces that cause them
Explain how conservation of angular momentum applies to martial arts
Describe the benefits of the Socratic Method in aiding student learning

Before Class:

Homework: Upload Problem Set #6 [T 2/8] to Canvas before class.
Textbook: Read Ch 5.0 - Central Attraction: Centripetal Acceleration [3.5 pg, 5 ex]
Video: Watch (Abridged) Centripetal Acceleration NOT Centripetal Force [8m24s]
Video: Watch Angular Momentum, Wheel Kick [9m4s]
Article: Read another NPR article about education (external)
- "The first step is to teach Socratically, by asking questions and having students think out loud. This works much better than lecturing."
- "Teachers who find their kids' ideas fascinating are just better teachers than teachers who find the subject matter fascinating."
Discussion: Please leave a statement or question on our Week 6 Reading Discussion
Only if interested about Physics of figure skating, listen to NPR https://www.npr.org/2022/02/04/1078181430/the-physics-of-figure-skating
See her do the quadruple spin! in a torque-free environment. I ask myself... as she's spinning at the end... it would be so lovely if she could just slow to a stop in that position... why doesn't she do that?

During Class:

We will observe objects experiencing centripetal acceleration
We will practice being careful with our semantics
We will discuss the race between a low friction cart and a hoop

Day 23 | Wednesday 2/9 | Universal Gravity

Let's review: Forces cause acceleration. These forces are NOT centripetal forces... they are the same forces that we know: gravity, tension, friction, normal force. There is also no such thing as centrifugal force. It is important that you absorb this idea and practice talking about central forces and centripetal acceleration without lapsing into weak semantics. Pay attention to how you phrase things...

Goals:

By the end of today you will be able to...

Explain what the inverse square law is and describe some situations where it applies
Describe how the law of universal gravitation applies to large objects like the Earth
Calculate some relevant parameters for Low-Earth and Geosynchronous orbits
Articulate what central forces are and are not

Before Class:

Video: Watch Gravity and Inverse Square Law [5m38s]
Textbook: Read Ch 5.1 - Ubiquitous Inverse Square Law: It's Everywhere! [2 pg, 2 ex]
Textbook: Read Ch 5.2 - Universal Gravity [2.5 pg, 3 ex]
Discussion: Please leave a statement or question on our Week 6 Reading Discussion
Video: Watch Gravity: Veritasium Music Video [3m54s]
Video: Watch Centrifugal Force? [3m38s]
Study: We will have our weekly assessment in class. Review what you have learned so far and look at the Problem Set #6 solutions to see how to improve. Follow the problem-solving rubric to know what to expect.

During Class:

We will practice applying the universal law of gravitation to various scenarios
We will take Weekly Assessment #6 [20 min]

Day 24 | Thursday 2/10 | Loop-the-loop

When we have circular dynamics with more than one force, it's just like the elevator problem, but the acceleration is centripetal acceleration. The loop-the-loop is a fun application of centripetal acceleration. Have you ever wondered why rollercoaster rides are shaped the way they are? Today we will explore this question and calculate the normal force on our bodies at different points in the loops. And if you're curious, you can see a detailed explanation of the rolling object physics.

Goals:

By the end of today you will be able to...

Calculate and compare the normal force at the top and bottom of a loop-the-loop
Describe the dynamics of objects moving along curved paths

Before Class:

Video: Watch Water Spinning Over Your Head [4m26s]
Textbook: Read Ch 5.3 - Loop-the-loop: Circular Motion in the Vertical Plane [4 pg, 7 ex]
- Please make sure you try Exercises 5.3.3, 5.3.4 and 5.3.5.
Video: Watch Skateboarding Loop of Death [1m35s]
Article: Read an NPR article about a Nobel Laureate's research on active learning (optional)
Discussion: Please leave a statement or question on our Week 6 Reading Discussion
Video: Watch this video from Flipping Physics (the interesting part is between 3:50 and 5:15 (optional))
Survey: Take this Short Survey - Day 24
Reflect: Be prepared to address the question, "when I stand on the scale on the equator and on the North Pole, where does the scale read more?"

During Class:

We will examine circular motion in the vertical plane with water buckets and loop-the-loops
We will explore how objects on curved paths accelerate

Week 6 Wrap-up

Central forces are of fundamental importance in physics. We have seen how the inverse square law in Newton's Universal Law of Gravitation keeps bodies in circular motion. We've also learned to be careful with how we describe the dynamics of circular motion, remembering that forces are pushes and pulls that CAUSE accelerations. We've applied these ideas to some interesting problems, like the loop-the-loop, and we've seen where they apply to objects following curved paths.

Next week we will look at gravity through the energy lens and learn about escape velocity from a potential well before moving on to consider systems of masses. We will examine the Atwood Machine, a system of pulleys and masses, and practice solving problems for systems as a whole.

For now, review our learning objectives for this week and consider where you might want to go back and review the concepts to gain a more solid footing. If you are feeling confident about this week's learning, reach out to a colleague and offer to help them if they are still feeling challenged. You will both benefit from the interaction.