## Centripetal Acceleration Notes - Section 2: Defining Centripetal Acceleration

# Uncorking Centripetal Force

Lesson 4 of 8

## Objective: Students will be able to define and experience centripetal force.

*50 minutes*

In the previous lesson, students developed an understanding of constant angular acceleration and the goal for today's lesson is to develop an understanding of centripetal acceleration and centripetal force. After I define centripetal force for students with a PowerPoint (in anticipation of covering HS-PS2-4), students see centripetal acceleration and centripetal force in action (SP 5 & 8) when they swing a cork over their heads and calculate the tension in the connected string. The lesson ends with students getting an opportunity to reflect and share thoughts in pairs.

In preparation for our centripetal acceleration activity, I organize and lay out one mass, one paperclip, about 1.5m of string, and a cork for each group. Having these materials ready to go before class allows the lesson to flow without interruption.

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It's time for students to take out their science notebooks and get ready to define centripetal acceleration and force. Students are introduced to the meaning of an object moving around a circle at constant speed, then derive the centripetal acceleration and force equations, and solve an example. My students are operating under the expectation that they must write down key points from the presentation. This expectation of how to take notes has been outlined and ingrained in their learning since freshman year, but we've practiced it quite a bit throughout earlier lessons in the course as well.

I display my Centripetal Acceleration presentation (also available in PPT) to help the students understand what they need to write down, but I also have a hard copy of the document in my hand. The printed copy includes notes (viewable only when the PPT file is downloaded) that I've written to myself to make sure I accomplish the learning goals as we work through the presentation. The nice thing about having a hard copy in my hand is that if I think of a great side-note or new example, I have the ability to write it down immediately. Having this hard copy also allows me to walk throughout the room as I ask students questions. For example, in the second slide, I ask students "How many times have we referred back to Newton's Second Law?" As we go through the notes, I welcome questions and expect participation from the students.

The presentation ends with a sample problem, so I make sure I use appropriate wait time for students to read the problem, think about their answers, and attempt to solve it in their notebooks. This process usually takes about three minutes, but then I ask students to be able to explain their answers. The explanation is the part that often stumps them, so I wait another minute or two before asking for student volunteers to share their ideas. Once we've successfully reached the answer through the discussion, I reveal the answers on the slide (each one becomes visible with a click of the mouse) and it's time to move into the next activity.

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#### Centripetal Cork Swing

*30 min*

During the previous class I assigned partners, so today I allow the students freedom in choosing lab partners. Groups of two to four seem to work best so that all students have an opportunity to be engaged in the activity. After they've chosen their groups, someone from each group needs to get a copy of the activity and the materials from the front of the room.

The procedure in the lab document is straight-forward, but I still make sure to circulate throughout the room and check-in with the groups. The goal of this activity is to show students how centripetal acceleration can be useful in a variety of situations, including calculating tension. Students start by attaching a cork to one end of the string and a mass to the other. They then swing the cork over their head so that it moves with constant circular motion while a partner times the number of revolutions. After three trials, students calculate the period of each trial and then use that to calculate the tension in the string. Finally, using the average tension from the three trials, students compare the tension with the weight of the mass that was hung at the bottom of the string and calculate the percent error.

I walk around the room offering encouragement as the students swing their corks, and ask questions such as "How is Newton's Second Law a part of this lab?" or "What is the direction of the cork's translational velocity?" Students understand the expectation that once they have completed collecting the data it's time to move into the analysis section. In fact, it's this analysis section and writing that earns students points for this activity. While the students do find it fun to see centripetal acceleration in action, the purpose of this lab is for students to use centripetal acceleration in the calculations of their lab write-ups.

When there is approximately 10 minutes prior to the end of class (5 minutes left of the time I've allowed for this activity), I ask students to put everything back the way they found it and return to their seats. I also tell them at this point that the lab is due at the start of the next class meeting.

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The closure for today starts by asking students to sit quietly and think about one word that describes the inertia activity. They get about a minute to quietly reflect, and then students turn to someone near them and share their word. I'm not overly strict on if students share with just one person or if they share in small groups, because I want everyone to be given an opportunity to participate. The goal of this closure is to provide students with an opportunity to debrief the lab activity and its application of centripetal acceleration.

I walk throughout the room during the quiet reflection time to ensure my students are focused, but I also walk as students are sharing with their neighbors. I ask students to share their words with me, so that I can check their level of understanding and reflect on my teaching practices. When I heard words such as "free body diagram," "acceleration," and "net force" I was confident that my students had grasped the content of today's lesson.

#### Resources

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- LESSON 1: Introduction to Angular Motion
- LESSON 2: Constant Angular Acceleration
- LESSON 3: Rotation of a Ladybug
- LESSON 4: Uncorking Centripetal Force
- LESSON 5: Deriving Universal Gravitation
- LESSON 6: Exploring Kepler's Three Laws
- LESSON 7: Reviewing Rotational Motion
- LESSON 8: Rotational Motion Test