## SCIENCE OF GOLF: Torque and Moment of Inertia - STEM Lesson Plan (Grades 7 - 12)

##### Objective:

Torque and moment of inertia are classical mechanics concepts and are central to a successful golf swing. Torque is a measure of how effectively a force causes rotation. An example is the golf club's shaft twisting as the club head swings towards the golf ball. Moment of inertia, or resistance to rotation, impacts golf by measuring the “forgiveness” of a golf club. Golfers would like to have golf clubs that are as forgiving as possible. What do the rules of golf have to say about that?

##### Introduction Notes:

Science OF GOLF: Torque and Moment of Inertia

Lesson plans produced by the National Science Teachers Association.

Video produced by NBC Learn in collaboration with the USGA and Chevron.

Background and Planning Information............................................................ 2

Video Timeline .............................................................................................................................. 2

Language Support ......................................................................................................................... 2

Next Generation Science Standards.............................................................................................. 19

Common Core State Standards for English Language Arts/Literacy................................................. 19

Promote STEM with Video............................................................................. 3

Connect to Science......................................................................................................................... 3

Connect to Technology................................................................................................................... 3

Connect to Engineering.................................................................................................................. 4

Connect to Math............................................................................................................................ 5

Explore Understanding................................................................................................................... 6

Identify Problems.......................................................................................................................... 7

Investigate Design Problems.......................................................................................................... 7

Materials and the Inquiry Process....................................................................................... 7

Open Choice Approach....................................................................................................... 8

Focused Approach............................................................................................................. 9

Media Research Approach................................................................................................ 11

Related Internet Resources.................................................................................. 12

Make a Claim Backed by Evidence................................................................................................. 12

Present and Compare Findings..................................................................................................... 12

Reflect and Redesign.................................................................................................................... 13

Inquiry Assessment...................................................................................................................... 13

Incorporate Video into Your Lesson Plan...................................................... 13

Integrate Video in Instruction....................................................................................................... 13

Bellringer......................................................................................................................... 13

Homework....................................................................................................................... 13

Using the 5E Approach...................................................................................................... 13

Connect to Physical Education....................................................................................................... 14

Connect to Economics.................................................................................................................. 14

Use Video as a Writing Prompt...................................................................................................... 14

Copy Masters .............................................................................................. 15

Assessment Rubric for Inquiry Investigations................................................................................ 18

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Science of Golf (SOG): Torque and Moment of Inertia discusses the major impact that both torque and moment of inertia can have on the motion of the golf ball and the game of golf. SOG: Torque and Moment of Inertia features LPGA golfer Belen Mozo, who has competed in more than 55 tournaments since her 2011 rookie year, and Matthew Pringle, Ph.D., Manager of Research and Development for Equipment Standards at the United States Golf Association. Pringle explains how the backswing portion of the golf swing builds torque in both the golfer's body and the golf club. Mozo demonstrates what she does to "smash it." A dynamic graphic provides a clear understanding of moment of inertia, something most golfers would like to have more of.

0:00     0:15     Series opening

0:16     0:33     Slightest change in golf swing mechanics….

0:33     0:53     Introducing Belen Mozo

0:54     1:03     Two key physics concepts are key to a top-notch swing

1:04     1:31     Introducing Matt Pringle and torque

1:32     1:37     Definition of torque and torque in the golf swing

1:38     1:54     Torque graphic and torque in Belen Mozo’s swing

1:55     2:08     Belen Mozo presents how she packs power into her swing

2:09     2:32     Introduction to moment of inertia

2:33     2:38     Matt Pringle explains moment of inertia

2:39     3:00     Definition of moment of inertia and comparison to tightrope walkers

3:01     3:12     Graphic: Golf club design; Matt Pringle discusses importance of larger moment of inertia

3:13     3:42     Advantage of a large moment of inertia and why USGA rules limit the size of the club head

3:43     4:03     Importance of the golfer to the swing

4:04     4:17     Summary

4:18     4:33     Closing credits

Language Support: To aid those with limited English proficiency or others who need help focusing on the video, click the Transcript tab on the right side of the video window, then copy and paste the text into a document for student reference.

Standards Connections for NGSS and Common Core ELA

Connected standards are listed in full on the last page of this document.

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Connect to Science

Torque and moment of inertia are classical mechanics concepts and are central to a successful golf swing. Torque is a measure of how effectively a force causes rotation. An example is the golf club's shaft twisting as the club head swings towards the golf ball. Moment of inertia, or resistance to rotation, impacts golf by measuring the “forgiveness” of a golf club. Golfers would like to have golf clubs that are as forgiving as possible. What do the rules of golf have to say about that?

Related Science Concepts

• acceleration

• angular momentum

• balanced torques

• center of gravity

• displacement

• force

• kinetic energy

• lever arm

• linear momentum

• Newton's Second Law

• rotational inertia

• vectors

• velocity

Take Action with Students

Students with only limited exposure to physics might explore torque using a simple lever system, as shared at: https://phet.colorado.edu/en/simulation/balancing-act. This simulation will allow students to quickly learn about torque. Students who have had some physics can also use this simulation. Instead of just manipulating the masses on the lever they can actually do calculations to determine the placement of the second mass when playing the game. The simulation can then serve as a quick check.

Students with a greater depth of knowledge might analyze the claims made during the graphic portion of the video.

Students can use http://www.usga.org/USGASearch.aspx?q=torque to examine other ways in which torque impacts the sport of golf. Students could create a technical manual to be shared with the class.

Middle school and high school students who have had some exposure to physics may be familiar with torque and moment of inertia. After viewing the video, have students write formal and operational definitions for both concepts. Typical graphite driver shafts twist from 2° (low torque) to 6° (high torque). Students might make predictions concerning the flight of a golf ball that was hit 300 yards. The low torque driver would tend to have the ball go closer to the target if hit correctly. High torque clubs have a bit of snap to them but are harder to control.

In the video Matt Pringle compares moment of inertia to the long pole that tightrope walkers use to maintain balance—low tech at best. Pringle said that the "very long pole creates a tremendous amount of moment of inertia" that helps the walker balance. Grand Canyon tightrope walker Nik Wallenda used a 43-pound, 30-foot-long pole to help with his balance as he crossed the 1,400-foot-long, 2-inch-thick steel cable. The long heavy pole, with its significant moment of inertia, increases the tightrope walker's rotational inertia. The real technology, that

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didn't get mentioned in the video, is the golf club itself. A shaft manufacturer states, "A piece of equipment often overlooked by golfers is the golf shaft, an integral part of the club that can greatly make a difference, positive or negative." In some cases, the shaft can be the most expensive part of a golf club.

Take Action with Students

Before watching the video have students discuss what they know about torque and moment of inertia. Have students discuss their ideas about how torque might be a consideration when constructing the shaft used in a golf club. They might look at http://entertainment.howstuffworks.com/sports/golf/basics/golf-club2.htm to see how their ideas compare with the functions that a golf club's shaft must fulfill.

For most of the history of golf clubs their shafts were made of wood. Only since 1930 have steel shafts been allowed by the rules. Graphite shafts first appeared in the 1970s. Students might discuss the valuable attributes of each of these materials and make predictions as to the benefits derived by golfers during the respective periods in which they were used. Students might use http://www.golfclubshaftreview.com/history-of-the-golf-shaft.html to see if their ideas were accurate.

The engineering design process involves identifying problems and finding solutions, usually as part of an ongoing cycle of innovation. High-end driver shafts can cost as much as \$1,000! That is a great deal of money for something with the simple purpose of connecting the grip held by the golfer to the head of the golf club. How would you calculate the cost to build a 43-pound, 30-foot-long balancing pole that would see you safely across a 1,500 foot deep chasm? See http://www.csmonitor.com/Science/2013/0624/Grand-Canyon-tightrope-walk-What-was-that-huge-pole-for

Take Action with Students

Part of the engineering design process involves creating a solution that is cost effective to manufacture. This is especially important when no one makes or sells the tool that you need. An extensive Internet search did not yield a single vendor for tightrope walking poles. It did yield information on a person that taught himself how to tightrope walk and had to resort to building his own balancing poles (http://www.stormbound.org/tightrope.html). This site has some interesting pictures that detail the different designs of his poles. Have students do research to suggest how to make a 50-pound, 40-foot-long balancing pole that a novice tightrope walker might afford. Considerations might include: how rigid the pole is; how much the pole can droop; what is the cost of its components; can it be broken down for storage; what materials might be best but would be too expensive; will it require a harness because of its weight; is it the optimal length.

Engineers frequently must comply with constraints that have to be considered when designing an innovation. Given the current rules of the game, have students pose possible designs for golf club shafts that would give a golfer an advantage.

Engineers frequently find solutions to their problems using composite (made of different materials) materials. Composite materials often have properties that are quite different than the constituent materials of which they are constructed. Have students list materials

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they are familiar with that might be used to create a golf club shaft that could solve the torque problem. Guide the class to list pros and cons of each material and give reasons why they might work well together and serve as a possible solution.

Math is involved in the calculation of both torque and the moment of inertia. Students may be used to just plugging numbers into a formula. Challenge students to make diagrams that demonstrate what is happening in each problems and the relationship to the formula they choose. Using the following as examples, challenge students to write their own problems, which they have to solve, before giving them to their peers.

Take Action with Students

Simple Torque Problems (Torque = F•l)

o   A mechanic uses a 17 mm boxed end wrench to turn a hexagonal nut with a 60 N perpendicular force at the end of the 0.21-m long wrench. How much torque was produced? When the nut wouldn't budge, a 0.65-m pipe was slid over the wrench down to the nut, and a good jerk applied 80 N to the end of the pipe. How much torque was produced by the longer lever?

o   A seesaw provides the classic situation for determining the torque of a system. Two students approach a perfectly balanced wooden seesaw. A student who can exert 600 N sits astride the seesaw 2 m from the fulcrum. Where would a student who can exert 400 N have to sit to balance her friend?

Torque Problems that Require Trigonometry [(sinY•l = F),(Torque = F•l)]

o   Many times, a force can't be applied perpendicular to the lever (i.e., the solution requires trigonometry). Another mechanic, working on a nut rusted on to a bolt on the underside of a car, applies an 80 N force at an angle of 30° to the end of a 2 m pipe placed over the correct sized wrench. How much torque is produced?

o   What force is required to produce a 40.0 N-m torque if the force is applied at an angle of 60°˚ at the end of a 4.0 m lever?

Torque Problems and Shaped Objects (see formulas at http://physics.about.com/od/RotationalMotion/tp/MomentOfInertiaFormulas.htm)

Moment of inertia is the measure of the amount of moment that has to be applied to an object to overcome its own inertia. Variables include the object’s shape, mass distribution, and the orientation of the axis the object will rotate about. Many websites offer formulas for a variety of shapes.

o   What is the moment of inertia of a solid sphere with a radius of 10- cm and a mass of 50- kg?

o   Find the moment of inertia of a long thin rod that is balanced about its center of mass with a length of 0.25- m and a mass of 10- kg.

Golf Problems

Grip it and rip it! Hit the big dog! At the time of this writing, the average driving distance for the PGA’s top ten 10 drivers of the golf ball is an astounding 307.31 yards! Imagine if one of these players was to hit one of an average drive with a driver that had a shaft with a torque that would cause the club head to be open (aimed to the right for a right-handed golfer, or

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closed—aimed to the left for a right-handed golfer) by 1°˚ at the moment it impacts the golf

ball. How far from where the golfer wanted to land would the ball fall? (Let’s assume that the wind is not blowing at the time.)

Encourage inquiry using a strategy modeled on the research-based science writing heuristic. Student work will vary in complexity and depth depending on grade level, prior knowledge, and creativity. Use the prompts liberally to encourage thought and discussion. Student Copy Masters begin on page 15.

Spark discussion using a tool or images (see the links that follow) or by demonstrating the torque that causes a golf club’s shaft to twist or resist twisting using straws or paper towel tubes that can be twisted to various degrees to find out what students know about torque and moment of inertia.

After breaking the ice on the topic you might move groups of students to the four corners of the room. In each corner, the group will discuss torque and moment of inertia (or an aspect of torque and moment of inertia that you’ve assigned to each corner) to activate their background knowledge. Four corners can be highly engaging for students and only requires 5 to 10 minutes. Use the following or similar prompts to start students talking.

One experience I have had with torque or moment of inertia is….

Torque is created by golfers when....

I experience torque or moment of inertia everyday when….

One way I think I could change the torque or moment of inertia of a golf club to make the design more forgiving is….

Things that affect torque or moment of inertia include….

Sometimes, torque makes things in golf more difficult, such as when….

Sometimes torque or moment of inertia is necessary, such as when....

The problem/solution torque causes in golf is ....

The problem/solution moment of inertia causes in golf is ....

The engineer/scientist can help golfers by....

Newer golf clubs may help lower scores for average or poor golfers because....

Some factors controlling moment of inertia are....

Show SOG: Torque and Moment of Inertia and encourage students to take notes about torque or moment of inertia and the recommendations made by experts while they watch. Continue the discussion of how a design team might improve the torque or moment of inertia of an object using the following or similar prompts:

When I watched the video, I thought about….

We learned from the video that….

One problem presented in the video was….

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The experts in the video explained that….

Variables influencing the potential solutions include….

Torque, during the golf swing, impacts the flight of the golf ball by….

Some golfers call moment of inertia the club’s "sweet spot" because….

Stimulate small-group discussion with the prompt: This video makes me think about these problems…. Then have small groups list questions they have about improving torque or moment of inertia. Ask groups to choose one question and phrase it in such a way as to reflect an engineering problem that is researchable and/or testable. Bring groups together to discuss/share their problems. Remind students that engineering problems usually have multiple solutions. Some sample questions that reflect engineering design problems are:

What factors can be changed that might limit torque or make it more useful?

What factors can be changed that might improve moment of inertia or make it more useful?

Why do the rules of golf limit changes that can be made to the golf club?

Would increasing/reducing the torque or moment of inertia improve performance?

How could we use _____ to improve performance?

What is the optimal way to design the shaft of a golf club?

Which has a greater effect? Improving the golf club or improving the athlete’s performance?

How can a design team predict how their improvements will impact the flight of a golf ball?

How might torque be maintained to optimize the flight of the golf ball?

Choose one of the following options based on your students’ knowledge, creativity, and ability level and your available materials. Actual materials needed would vary greatly based on these factors as well.

Allow time for students to examine and manipulate the materials that are available. Doing so aids students in refining their questions or prompts new ones that should be recorded for future investigation.

Students might use the following materials to explore these video-related topics:

moment of inertia using a top: paper clips (different sizes), metal coat hangers, compact discs, pencils (different diameters), cardboard, reusable adhesive, modeling clay, tongue depressors or craft sticks, tape, straws, plastic bottles, glue, and paper for folding or assorted toy tops

moment of inertia using a student designed golf club: meter sticks (golf club shaft), wooden blocks (in pairs by size), rubber bands, masking tape, large wooden dowels (or round broom sticks), golf balls, bag ties, smaller blocks of wood, metal washers (or other weights), equal sized clumps of clay, and large pieces of paper on which to track the path of the golf ball

Measuring tools such as meter sticks, stopwatches, magnifying lenses, electronic balances, spring scales, smart phone video cameras, graduated cylinders, protractors, rulers or measuring

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tape, and calculators might also be useful in the design process.

Safety Considerations: You and students should wear cover goggles. Spin tops on a flat surface away from students’ faces. Students should suspend their “golf clubs,” pendulum fashion, to allow the force of gravity to supply a limited hit. Review safe use of tools and measurement devices as needed. Augment your own safety procedures with NSTA’s Safety Portal at http://www.nsta.org/portals/safety.aspx.

1.      Give students time to discuss their various questions. Groups might agree on one problem for which they will design a solution, or each group might evaluate different problems and solutions. Some ideas include designing a top with a moment of inertia that will allow it to spin for the longest time, or modeling a golf club’s shaft using composite materials to determine a torque that will allow a ball to hit within a desired target. To help students envision their investigations, use prompts such as the following:

The design problem we are solving is….

Materials we could use to implement our design are….

We are designing a solution that will….

Barriers to success that we anticipate are….

Acceptable evidence for a successful solution would include….

2.      Lead discussions to establish the criteria and constraints within which solutions might be designed. Remind students that criteria are factors by which they can judge the success of their effort and that constraints are limitations to the effort and are often related to materials, time, or money.

We think we can solve the problem by....

Our criteria for success are _____ and we determine them by....

Constraints that might limit potential solutions are....

Innovative design features we will include are….

3.      Have students determine the dependent variable they will use to evaluate their design. Check the students' understandings of each variable, such as spin rate, spin duration, or off-line hits. To do this, have students determine other variables associated with the problem they are trying to solve. Then have them determine what data/evidence they need to collect to evaluate the success of their design.

4.      Students should brainstorm a plan for their evidence collection. Work with students to develop safe procedures that control variables and enable them to make accurate measurements. Insist that they get your approval on their procedures before they start any investigation. Encourage students with prompts such as the following:

Information we need to understand before we can start our investigation includes....

We will change our composite club shaft to....

We will test our prototype or model by….

We will make design decisions, or changes to the independent variable, such as _____ to observe what happens to the dependent variable.

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The data we will collect are….

We will record and organize our data using….

5.      Allow students to spend some time working with the materials they have decided to use to implement their design. As students work with the materials, suggest that they reexamine their problem(s) and write down the procedures they intend to follow and how they will test their design and collect the data necessary to revise their design. Collecting evidence to promote future iterations and innovations is a critical step in the engineering design cycle. Guide students with prompts such as the following.

Information we need to understand before designing our composite club shaft includes….

We will construct our prototype or model by….

While constructing our prototype or model we will….

To conduct our investigation safely, we will….

We will represent our data by….

Mathematical models we can use in our investigation include….

6.      Be sure to work with students to develop safe procedures that keep the variables not being tested constant, allowing students to make accurate measurements.

7.      After communicating information to the class about their solution and reflecting on their own solution, as well as those of other groups, allow the class or small groups to go through a redesign process to optimize their solutions and what they have learned.

The following exemplifies ways students might design solutions to a problem involving moment of inertia. Give students leeway in determining exactly how they will build and test their design, but insist that they get your approval on their procedures before they start any investigation. You might include constraints for issues of safety, time, or materials.

Overview: To explore moment of inertia using tops, students might modify a top’s moment of inertia so that it will spin for the greatest possible duration or have the best balance. If tops are available, moment of inertia can be changed by adding sticky clay or reusable adhesive to the top’s shoulder according to the student’s chosen strategy. If tops are not available, students might make their own following instructions from websites such as http://www.youtube.com/watch?v=-9N4B87DpQc&feature=related (students could make larger tops by increasing the size of the paper they start with) and http://www.instructables.com/id/44-Fanciful-Uses-for-Dud-Discs/step2/Spinning-tops/ . Students might then add to their tops using materials such as tongue depressors to extend the top’s moment of inertia. Students could have a “spin off” in which the last top standing has the best balance. Students would need to follow steps similar to those that follow below to complete and test their design solutions.

To explore moment of inertia using a golf club, students might design a system like the one in the photograph. The stools could be replaced by ring stands. Materials can be substituted based on what is available in the classroom.

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1.      Give students time to discuss their selected problem(s). Allow time for groups to examine all of the materials available to them. Guide whole-class or small-group discussions to identify the problem being solved and then to identify criteria and constraints against which solutions will be developed. For example, the golf club students create should have the shape of a golf club, but some liberties in attaching the head to the shaft should be allowed. Remind students that criteria are factors by which they can judge the success of their effort and that constraints are limitations to the effort and are often related to materials, time, or money. Use prompts such as the following:

The problem we are solving is….

We are designing a solution that will….

The science concepts that we will need to use in creating our design include….

We think we can solve the problem by....

Our criteria for success are....

Constraints that might limit potential solutions are....

We will design our model to....

Acceptable evidence that would support our claims of success for our design includes….

2.      Encourage students to think about how they can design and construct their model golf club with the most advantageous moment of inertia considering variables such as mass, location of weights, width of club face, the point on the club face that strikes the ball, and force with which the ball is hit. Use prompts such as the following:

The problem we are solving is....

Factors influencing the moment of inertia include….

We can build a model of a golf club using….

In the video, the club was designed to take advantage of the moment of inertia by….

Our model golf club will be able to....

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One thing we will need to do with the golf club’s shaft is....

One thing we will need to do with the golf club’s head is....

We’re not going to use _____ because we think it/they will….

Increasing/decreasing the mass of the head of the golf club will....

Increasing/decreasing the length of the head of the golf club will....

We think ourchanges will increase the momentof inertia because....

The model we have designed is similar/dissimilar to an actual golf club because….

Constraints that might limit the range of potential solutions are….

3.      Students should brainstorm a plan for evidence collection prior to designing their golf club. Provide students with the following prompts to guide how they will collect evidence for evaluating their design:

We will test our design by….

We will change the golf club design in the following ways to see the relationship to the dependent variable….

The data (dependent variable) we will collect are….

We will track the path each golf ball follows by….

We will record and organize our data using….

We will use evidence such as _____ to determine the need for additional changes, such as….

4.      Students plan and design their model golf clubs from the materials at hand. Students might design and build their golf clubs similar to the system shown above,or materials can be substituted based on what is available.The head of the golf clubs might also be designed from a single piece of metal (on which weights can be hung) , or a combination of other materials. The shaft of the golf club might be replaced by a dowel, a metal or PVC tube, or other materials. Some students may address the issue of torque in the shaft of the model golf club. Some students might attach the head of the golf club in a much more rigid fashion. On the basis ofconstraints identified for this activity, students may also make adjustments to where the shaft attaches to the head of the golf club (some putters have stafts that connect to the center of the putter head). Encourage multiple trials of the golf club hitting the golf ball from the same or various points on the club face with the same force. Each student, or group of students, should use the same golf ball for all trials during this activity. Those that are interested in precision might use a marker to place a dot on the golf ball so that it can be struck in the same place every time.

5.      After communicating information to the class about their solution and reflecting on their own solution as well as those of other groups, allow the class or small groups to go through a redesign process to improve those solutions.

Common Core State Standards Connections: ELA/Literacy –

RST.6-8.1 Cite specific textual evidence to support analysis of science and technical texts, attending to the precise details of explanations or descriptions

WHST.6-8.1 Write arguments focused on discipline-specific content.

WHST.6-8.7 Conduct short research projects to answer a question (including a self-generated question), drawing on several sources and generating additional related, focused questions that allow for multiple avenues of exploration.

WHST.6-8.8 Gather relevant information from multiple print and digital sources, using search terms effectively; assess the credibility and accuracy of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and following a standard format for citation.

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Groups might have questions that are best explored using print media and online resources. Students should brainstorm to form a list of key words and phrases they could use in Internet search engines that might result in resources that will help them answer the question. Review how to safely browse the Web, how to evaluate information on the Internet for accuracy, and how to correctly cite the information found. Suggest students make note of any interesting tangents they find in their research efforts for future inquiry. Encourage students with prompts such as the following:

Words and phrases associated with our question are….

The reliability of our sources was established by….

The science and math concepts that underpin a possible solution are….

Our research might feed into an engineering design solution, such as….

To conduct a safe investigation using the Internet, we will….

As students carry out their design investigations, ensure they record their observations and measurements. Students should analyze their observations in order to state one or more claims. Encourage students with this prompt: As evidenced by… I claim… because…. or I claim our design (was/was not) successful because….

An example claim might be:

As evidenced bymultiple trials in which there were a majority of on-line hits, I claim that a stiff composite golf club shaft had less torque, whereas other golf club shafts with greater torque had more off-line hits.

Encourage students to prepare presentations that outline their inquiry investigations so they can compare results with others. Students might do a Gallery Walk through the presentations and write peer reviews, as would be done on published science and engineering findings. Students might also make comparisons with material they find on the Internet, information presented in the video, or an expert they chose to interview. Remind students to credit their original sources in their comparisons. Elicit comparisons from students with prompts such as:

My findings are similar to (or different from) those of the experts in the video in that….

My findings are similar to (or different from) those of my classmates in that….

My findings are similar to (or different from) those that I found on the Internet in that….

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Students might make comparisons like the following:

My results were different from those discussed in the video in that although the golf club in the video had some torque and would change direction after hitting the ball, the ball would fly in the correct direction, whereas the club head we designed had almost no moment of inertia and the ball always went off in the wrong direction.

Students should reflect on their understanding, thinking about how their ideas have changed or what they know now that they didn’t before. They should also evaluate their own designs in light of others’ presentations and propose changes that will optimize their designs. Encourage reflection, using prompts such as the following:

My ideas have changed from the beginning of this lesson because evidence showed that….

My design would be more effective if I _____ because I learned that….

My ideas changed in the following ways….

I now understand better or could teach another student….

See the rubric included in the student Copy Masters on page 18.

Bellringer:Show http://www.youtube.com/watch?v=zgwwOJ0B964. The video will be just as effective on an individual classroom computer that students can access as they arrive. Have students compare the device in the YouTube video to the graphic shown in SOG: Torque and Moment of Inertia (1:37–2:04). You might also explain that Titleist, a major manufacturer of golf clubs, actually offers a wrench that has the same function as that seen in the YouTube video. Have students suggest how such a tool helps help golfers.

Homework: Given: (Torque = F•l) if the force is applied at 90˚; and (sinY•l = F) if the force is not applied at 90˚] have students find the most interesting object at home for which they can write and solve a torque word problem. They might print their problem on one side of a piece of paper (along with data required to determine torque) and the solution on the other. Students might use their phone's camera to take a picture of the item they selected. Then in class, students can share their photos and problems, or exchange them in a challenge competition.

If you use a 5E approach to lesson plans, consider incorporating video in these Es:

Explore: Use the Design Investigations section of Facilitate Inquiry to support your lessons on torque and moment of inertia. Main concepts should include how torque and moment of inertia impact both sports and everyday life. Students could do research and make observations that can later be shared.

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Elaborate: In the video many slow-motion camera shots show the golf swing in action. Matt Pringle maintains, “The golfer’s body is applying a torque to their own body as well as the club and eventually to the club head.” Torque is applied to the arms (the upper pendulum arm) at the shoulders, and to the club (the lower pendulum arm) at the wrists or hands. In some shots, arm muscles can be seen flexing or under tension. Have students hold a golf club (or meter stick or broom) in various positions shown in the golf swing, while other students restrain the club to keep it from moving. At each point, try to identify which muscles are exerting force.

In golf, torque and moment of inertia problems have been dealt with through the use of special materials and rules that place limits on the shape and size of golf club head. Have students connect what they learned in SOG: Torque and Moment of Inertia to other sports that they have played, with prompts such as the following:

As evidenced in _____ a better way to deal with torque and moment of inertia might be….

The sport of _____ differentiates the equipment for pros and amateurs by....

I can compare and contrast how torque is generated in different sports by….

Other sports use torque (or inertia) by….

The video mentions ways in which torque and moment of inertia have been dealt with in the game of golf. Use what you've learned about cost-benefit analysis, incentives, competition and markets and prices to analyze and report on one of the following questions and prompts:

How does one determine if a change to the torque or moment of inertia is of benefit to the 29,000,000 American amateur golfers?

Criteria that might be used by the USGA when deciding to place/not place restrictions on moment of inertia are….

The costs and benefits of the USGA making a ruling that might make the game of golf more difficult for pros and everyday golfers alike might include....

What does it cost in equipment and fees for an amateur golfer to play one 18-hole round of golf per week for x years?

After students watch SOG: Torque and Moment of Inertia tell them that currently, about 560 golfers play on the PGA Tour. In the United States about 29,000,000 other players golf recreationally or for work. Right now, the USGA is trying to deal with what it sees as a problem that threatens the game of golf. The men on the Tour are hitting the ball too far. To solve this problem, USGA is thinking about placing limits on the moments of inertia (size of the club head) of drivers. This will be a decision that will impact all of the golfers in the United States. After viewing the video, encourage student writing with prompts such as the following.

The size of the club head, which affects moment of inertia, should be limited because....

Moment of inertia should not be limited because....

A good way to solve this problem for all golfers would be....

Compare and contrast, in light of this problem, the USGA efforts to protect the game of golf (an acceptable hit with the driver should not be longer than 290 yards) and the desire of golfers to make the game as easy as possible (I want to hit the ball 400 yards).

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Torque and Moment of Inertia

Use this as a guide to design and test your solution to a problem that you have indentified according to criteria and constraints established by the class. Record all of your notes and observations in your science notebook.

Identify Problems

Our class discussion and the video make me think about problems such as….

The materials we will use include….

Our criteria for success are….

Acceptable evidence for a successful solution would include….

The constraints within which we will work are….

We will record and organize our data using….

To conduct our investigation safely, we will….

Record and organize your data and observations from your tests using sketches, tables, and/or graphs.

Make a Claim Backed by Evidence

Analyze your results and make one or more claims based on the evidence your data shows. Make sure that the claim goes beyond summarizing the relationship between the variables.

 My Evidence My Claim My Reason

Present and Compare Findings

Listen to presentations of other groups and create a peer review as scientists do for one another. You might also compare your findings with those of experts in the video or that you have access to, or to material on the Internet. How do your findings compare? Be sure to give credit to others when you use their findings in your comparisons.

My findings are similar to (or different from) the experts in the video in that….

My findings are similar to (or different from) my classmates in that….

My findings are similar to (or different from) what I found on the Internet in that….

Reflect and Redesign

I claim that my ideas have changed from the beginning of this lesson in that….

My design would be more effective if I _____ because I learned that….

In redesigning, innovations we incorporated included….

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Torque and Moment of Inertia

Use this as a guide to design and test a model golf club according to criteria and constraints established by the class. Record all of your notes and observations in your science notebook.

Why are torque and moment of inertia an important consideration in the design of golf clubs?

Identify Problems

How can we make a golf club that has a larger moment of inertia?

What factors should we consider changing?

How can we be certain that the golf club we design will be an accurate model of a golf club?

Discuss with your group how you might make a model golf club from the materials available. Use these prompts to help you.

The science concepts that we will need to use in creating our design include….

We think we can solve the problem by....

Our criteria for success are....

Constraints that might limit the range of potential solutions are....

Acceptable evidence that would support our claims of success for our design include….

We will limit/increase torque/moment of inertia by....

We think these changes willincrease/decrease the moment of inertiaof the golf club because....

We will represent our data in the following way(s)….

We will track the path of each golf ball by….

We will compare the data from each trial by….

We will analyze the overall data by….

To conduct our investigation safely, we will….

Record and organize your observations and data in tables such as the one below. In the “Design Changes/Trial #” column describe the changes you made to your golf club so that it hit the ball toward your target. Make sketches of each change you make to your design.

 Design Iteration Describe Changes/Trial # Impact Point on Club Face Location of Weights Distance from Target (m) 1 Trial 1 Trial 2 Trial 3

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 2 Trial 1 Trial 2 Trial 3

Ideas for Analyzing Data

Describe how the changes you made to your golf club design impacted how far the ball went.

Describe how your data helped you make decisions to change your golf club.

What changes made the greatest impact on effectiveness of the golf club?

Make a Claim Backed by Evidence

Analyze your data and then make one or more claims based on the evidence your data shows. Make sure that the claim goes beyond summarizing the relationship between the variables.

 My Evidence My Claim My Reason

Present and Compare Findings

Listen to presentations of other groups and create a peer review as scientists do for one another. You might also compare your findings with those of experts in the video or that you have access to, or to material on the Internet. How do your findings compare? Be sure to give credit to others when you use their findings in your comparisons.

My findings are similar to (or different from) those of the experts in the video in that….

My findings are similar to (or different from) those of my classmates in that….

My findings are similar to (or different from) information I found on the Internet in that….

Reflect and Redesign

I claim that my ideas have changed from the beginning of this lesson in that….

My design would be more effective if I _____ because I learned that….

One part of the investigation I am most proud of is….

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 Criteria 1 point 2 points 3 points Initial problem Problem had only one possible solution, was off topic, or otherwise was not researchable or testable. Problem was researchable or testable but too broad or not answerable by the chosen investigation. Problem was clearly stated, was researchable or testable, and showed direct relationship to investigation. Investigation design The design of the investigation did not support a response to the initial question or provide a solution to the problem. While the design supported the initial problem, the procedure used to collect data (e.g., number of trials, or control of variables) was insufficient. Variables were clearly identified and controlled as needed with steps and trials that resulted in data that could be used to answer the question or solve the problem. Variables (if applicable) Either the dependent or independent variable was not identified. While the dependent and independent variables were identified, no controls were present. Variables identified and controlled in a way that resulting data can be analyzed and compared. Safety procedures Basic laboratory safety procedures were followed, but practices specific to the activity were not identified. Some, but not all, of the safety equipment was used and only some safe practices needed for this investigation were followed. Appropriate safety equipment used and safe practices adhered to. Data and Analysis (based on iterations) Observations were not made or recorded, and data are unreasonable in nature, or do not reflect what actually took place during the investigation. Observations were made, but were not very detailed, or data appear invalid or were not recorded appropriately. Detailed observations were made and properly recorded and data are plausible and recorded appropriately. Claim No claim was made or the claim had no relationship to the evidence used to support it. Claim was marginally related to evidence from investigation. Claim was backed by investigative or research evidence. Findings comparison Comparison of findings was limited to a description of the initial problem. Comparison of findings was not supported by the data collected. Comparison of findings included both methodology and data collected by at least one other entity. Reflection Student reflection was limited to a description of the procedure used. Student reflections were not related to the initial problem. Student reflections described at least one impact on thinking.

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Science OF GOLF: Torque and Moment of Inertia

Standards Connections

The following inquiry investigations might be part of a summative assessment for these performance expectations. See NGSS documents for additional related Common Core State Standards for ELA/Literacy and Mathematics.

MS. Forces and Interactions

MS-PS2-2. Plan an investigation to provide evidence that the change in an object’s motion depends on the sum of the forces on the object and the mass of the object.

Engineering

MS-ETS1-1. Define the criteria and constraints of a design problem with sufficient precision to ensure a successful solution, taking into account relevant scientific principles and potential impacts on people and the natural environment that may limit possible solutions.

MS-ETS1-2. Evaluate competing design solutions using a systematic process to determine how well they meet the criteria and constraints of the problem.

MS-ETS1-4. Develop a model to generate data for iterative testing and modification of a proposed object, tool, or process such that an optimal design can be achieved.

HS-ETS1-2. Design a solution to a complex real-world problem by breaking it down into smaller, more manageable problems that can be solved through engineering.

HS-ETS1-3. Evaluate a solution to a complex real-world problem based on prioritized criteria and trade-offs that account for a range of constraints, including cost, safety, reliability, and aesthetics, as well as possible social, cultural, and environmental impacts.

Science and Engineering Practices: Developing and Using Models

Develop a model to predict and/or describe phenomena.

RST.6-8.1 Cite specific textual evidence to support analysis of science and technical texts, attending to the precise details of explanations or descriptions

RST.6-8.3 Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks.

WHST.6-8.1 Write arguments focused on discipline-specific content.

WHST.6-8.7 Conduct short research projects to answer a question (including a self-generated question), drawing on several sources and generating additional related, focused questions that allow for multiple avenues of exploration.

WHST.6-8.8 Gather relevant information from multiple print and digital sources, using search terms effectively; assess the credibility and accuracy of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and following a standard format for citation.

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