The Arizona STEM Acceleration Project

The Magic of Euler’s Disk

The “Magic” of Euler’s Disc

A 5th grade STEM lesson

Kelly Coakley-Magid

05/19/24

Notes for teachers

There are a few versions of spinning disks on Amazon and you could get a few different ones and allow students to use them in their own experiment comparing the design and spin of each to extend this even further or as a possible science fair idea.

List of Materials

• Paper
• Pencils
• Timer or timers
• At least one Euler’s Disk
• Quarters and other coins
• Rolls of masking tape
• Optional: Hashtag building blocks from Target (similar to Plus Plus Blocks)

Standards

Also includes science and engineering practices:

● plan and carry out investigations ● analyze and interpret data

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Cross Cutting Concepts:

● cause and effect

● structure and function

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Standards

5th Grade Science 5.P3U2.5 Define problems and design solutions pertaining to force and motion.

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5th Grade Math: 5.MD.B Represent and interpret data. 5.MD.B.2 Make a line plot to display a data set of measurements in fractions of a unit (1/8, 1/2, 3/4). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

Objectives:

- Students will understand the science behind Euler's Disk and how it combines motion, friction, and gravity.

- Students will observe and describe the effects of motion, friction, and gravity on the spinning of Euler's Disk.

- Students will make predictions and formulate questions based on their observations.

- Students will engage in a hands-on activity to explore the properties of Euler's Disk.

- Students will practice data analysis by creating a line plot based on their measurements.

Agenda (lesson time)

This will take about four 40 minute sessions. It could easily take more. You could extend the engineering activity to have students create a package, logo, and directions for the spinner they design.

Intro/Driving Question/Opening

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Take out the Euler’s Disk. Show the two parts to students. Tell them you will spin the disk and time how long it takes to stop spinning. Ask students to write down a prediction of how long the disk will spin before it stops. Have students record their predictions if you like. Feel free to really up the stakes by offering to allow the person who has the closest guess have a turn at spinning the disk to see if they can beat your time. Be sure to do this in a place where all can see or use a doc cam. Encourage students to listen to the sounds the disk is making throughout the spin. The opening question is “How long do you predict this object will stay in motion when I twist it to spin?”

Hands-on Activity Instructions

• After the first spin and checking predictions to actual outcome, have students take out their notebooks and record what they notice and what they wonder about the spinning disk as you invite the student with the closest prediction to come up and spin the disk. Tell students to write as much as they can. They can also include a “What I think is happening” column on their notebook page if so inclined.
• Students will hopefully notice the sound, the texture, the student who spins it will definitely shout out “It is so heavy!” and they can record that.

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• Tell students they are going to make 3 line plots. They are going to work as a team of 3 to spin 3 different objects multiple times.
• Students should create 3 line plots, one for the quarter, one for the masking tape roll, one for the Euler’s Disk.
• Discuss fractions of a minute. You may wish to have students round to the nearest fraction as they record their time for the line plot.

You can work with students to create fractions to represent each second in a minute or you can use the one on the next slide. Have students put the fractions in order from least to greatest if they do not have the same denominator.

Fraction of a minute

• 3 seconds = 1/20

6 seconds = 1/10

10 seconds = ⅙

15 seconds = ¼

20 seconds = 1/3

30 seconds = ½

36 seconds = 3/5

45 seconds = ¾

48 seconds = ⅘

51 seconds = 17/20

57 seconds = 19/20

• Students should retrieve the materials (quarter, roll of masking tape, a timer and a Euler’s disk.
• Class needs to agree that they are testing the items on the same surfaces OR you can divide the teams and ask them to test on different surfaces and compare results later.
• Students should spin, time, and record each item a minimum of three times per item. If they have time for more, they should record more.
• After the results are recorded, the results should be displayed 3 line plots per group. These line plots should be checked by the teacher as the testing and recording occurs in class. The immediate feedback is needed to be sure students are not making huge errors in recording. For example, you want to be sure they are recording minutes, seconds, and fractions of a second. You may not want to use the fraction of a second and just stick to minutes and seconds. Be sure labels and titles on line plots are accurately displayed.

As students compare line plots, they should notice which objects spun for the longest amount of time. Have students discuss why they think some were spinning so much longer than others. Ask the students what they notice about the design of each object. Invite them to test and record other objects they think might have a long spinning time.

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Spend time discussing the Euler’s disk:

• Named after the Swiss mathematician Leonhard Euler.
• Explain to students that Euler's Disk uses physics to keep spinning.
• - Discuss how motion, friction, and gravity play a role in the spinning of the disk.
• - Explain that the disk spins faster as it flattens out and ask students to predict why this might happen.
• 3. Understanding Motion and Friction (10 minutes)
• - Explain that motion is the movement of the disk and friction is the force that slows it down.
• - Discuss examples of friction in everyday life and ask students to share their ideas.
• - Explain that the disk has less friction at the center, which allows it to keep spinning.
• - Ask students to think about why this might be the case and discuss their ideas as a class.

• 4. Gravity's Role in the Spin (5 minutes)
• - Explain that gravity pulls the disk towards the table and helps it stay in a circular path.
• - Discuss how gravity and the disk's shape create a stable spin.
• - Ask students to think about how gravity helps us in sports or other activities and share their ideas.

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• 5. The Shape of Euler's Disk (5 minutes)
• - Explain that Euler's Disk is a perfect circle with a slight dome shape.
• - Discuss how this shape helps distribute weight evenly and allows for a smooth and long-lasting spin.
• - Ask students to think about other objects that have shapes that help them move in special ways and share their ideas.

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• 6. Precession: A Wobbly Path to Stability (5 minutes)
• - Explain that precession is the wobbly motion as the disk spins.
• - Discuss how precession is caused by the disk trying to stay balanced.
• - Explain that this wobble actually helps keep the disk spinning longer.
• - Ask students if they have seen precession in other spinning objects, like a top, and discuss their observations.

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• 7. Energy Transfer in Euler's Disk (5 minutes)
• - Explain that the disk starts with potential energy and as it spins, energy changes to kinetic (motion) energy.
• - Discuss how some energy is lost to sound and heat due to friction.
• - Ask students to think about what happens to the energy of a ball when you throw it and share their ideas.

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• 8. The Sound of Euler's Disk (5 minutes)
• - Explain that as the disk spins, it makes a humming sound.
• - Discuss how the sound gets louder and higher-pitched as it spins faster.
• - Explain that this is due to the increasing speed of vibrations.
• - Ask students to think about why the pitch of the sound changes as the disk spins faster and share their ideas.

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Have students make connections front he above ideas to why the disk, quarter, and tape had different times.

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Next, challenge students to use materials in the room to design a spinner.

• Students should work in teams of two or alone.
• Students should draw and or write about their design before they build it.
• Allow one class period to design and build the spinning toy.

Suggested materials for building a spinning toy disk:

• foil
• masking tape
• quarters
• hashtag blocks
• clay
• play doh
• popsicle sticks
• dowels

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During the next class period, have students spin and record their times for their newly created objects. Students should then display the data in a line plot. Have students compare times to see who created the best spinner. Have students create a package and logo for their new design if desired.

Understanding Motion and Friction

• Motion is the movement of the disk.
• Friction is the force that slows the disk down.
• The disk has less friction at the center, which keeps it spinning.
• What are some examples of friction in everyday life?

Gravity's Role in the Spin

• Gravity pulls the disk towards the table.
• It helps the disk stay in a circular path.
• Gravity and the disk's shape create a stable spin.
• How does gravity help us in sports or other activities?

The Shape of Euler's Disk

• The disk is a perfect circle with a slight dome shape.
• This shape helps distribute weight evenly.
• It allows for a smooth and long-lasting spin.
• What other objects have shapes that help them move in special ways?

Precession: A Wobbly Path to Stability

• Precession is the wobbly motion as the disk spins.
• It's caused by the disk trying to stay balanced.
• This wobble actually helps keep the disk spinning longer.
• Have you seen precession in other spinning objects, like a top?

Energy Transfer in Euler's Disk

• The disk starts with potential energy.
• As it spins, energy changes to kinetic (motion) energy.
• Some energy is lost to sound and heat due to friction.
• What happens to the energy of a ball when you throw it?

The Sound of Euler's Disk

• As the disk spins, it makes a humming sound.
• The sound gets louder and higher-pitched as it spins faster.
• This is due to the increasing speed of vibrations.
• Why do you think the pitch of the sound changes as the disk spins faster?

Assessment

As an assessment, challenge students to use and object in the classroom (the hashtag blocks from Target are amazing for making tops!) to act as a spinning toy. Have students record the times that their object was able to spin for on three or more trials using a timer. Have students display this data in a line plot with a title and labels.

Hashtag blocks from Target (in the dollar section)

Differentiation

Create the outline of the line plots for students who may need a head start, have students partner up with a peer who will be helpful in recording, supply a chart of fractions and seconds or create one with students.

Remediation

Extension/Enrichment

Ask students to create and conduct their own experiment with the Euler’s disk and other objects.