Sponsored Content NBC News Learn is a former division of NBC News ‐ distributing the journalism and storytelling of NBC News to students in the classroom, at home, and in the community. Physics of the Golf Swing – STEM Lesson Plan (Grades 6-12) June 10, 2020 | 28 minutes, 1 second read This document is a companion piece to video titled Physics of the Golf Swing and is intended as a resource for educators. Background and Planning Information About the Video This video discusses how torque, centripetal force, and the double-pendulum effect combine to produce high club head speed during a golf swing. It features interviews with professional golfer Paula Creamer, amateur golfer Mike Miller, and John Spitzer, Managing Director of Equipment Standards for the United States Golf Association (USGA). Video Timeline 0:00 0:15 Series opening 0:16 0:37 Pointing out the importance of the drive in golf 0:38 0:55 Introducing John Spitzer and torque, centripetal force, and the double-pendulum effect as factors in the golf swing 0:56 1:14 Introducing Paula Creamer, Mike Miller, and the phantom camera 1:15 1:50 Connecting Paula Creamer’s drives to the double-pendulum effect 1:51 2:40 Illustrating a pendulum and John Spitzer’s explanation of how the double-pendulum effect applies to the golf swing 2:41 3:42 Using Mike Miller’s swing to illustrate centripetal force 3:43 4:37 Illustrating torque via the golf swing 4:38 4:50 Summarizing the combined roles of torque, centripetal force, and the double pendulum effect in a golf swing 4:51 5:07 Closing credits Language Support To aid those with limited English proficiency or others who need help focusing on the video, click on the Transcript tab on the side of the video window, then copy and paste into a document for student reference. Next Generation Science Standards Consider the investigation described in Facilitate SCIENCE Inquiry section as part of a summative assessment for the following performance expectations. Refer to a NGSS document for connected Common Core State Standards for ELA/Literacy and Mathematics. Engineering Design 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. Science and Engineering Practices Plan and conduct an investigation individually and collaboratively to produce data to serve as the basis for evidence, and in the design decide on types, how much, and the accuracy of data needed to produce reliable measurements. Consider limitations on the precision of the data (e.g., number of trials, cost, risk, time), and refine the design accordingly. Analyze data using tools, technologies, and/or models (e.g., computational, mathematical) in order to make valid and reliable scientific claims or determine an optimal design solution. Use mathematical representations of phenomena to describe explanations. Apply scientific ideas to solve a design problem, taking into account possible unanticipated effects. (page 1) Promote STEM with Video Connect to Science Torque and centripetal force are concepts in the science of mechanics, a branch of physics. The double pendulum is a slightly more complex version of the basic physics idea of a pendulum. Students taking physics or even physical science will likely have learned these concepts, but application of them to everyday practical situations will deepen students’ understanding. Take Action with Students To help students visualize torque, ask them to identify the factors involved in how a wrench works. They should identify two of these as the force applied to the wrench and the length of the wrench (or distance from the pivot point to the point of application of the force). Another factor is the direction of application of the force, which is most effective when perpendicular to the lever arm. Supply different wrenches and ask the students to investigate and compare how easy or difficult it is to use them. Ask students to identify the agent of the force that keeps a car going in a circle on a curved road; a ball going in a circle on the end of a string; or an airplane going in a circle while making a banked turn. Guide students to understand that in each case, the force points towards the center of the circle, and that the commonly-imagined outward centrifugal force is an illusion (existing only from the standpoint of an accelerated frame of reference). Give students kinesthetic experience with a double pendulum: have student make a very simple one by attaching two unsharpened pencils with a very short piece of string. Have them observe the behavior of the bottom one when the two are released in a variety of ways. Ask them if they think the bottom end could ever go faster than a single pendulum of the same total length would allow, and allow them to try it. Connect to Technology The concept of how your distance from the ball influences the distance the ball flies – discussed in Science of Golf (SOG): Physics of the Golf Swing from 3:23–3:40 – contributes to the technology of golf club design. Over time, driver shafts have lengthened by two to three inches in the belief that “every little bit helps.” Take Action with Students Have students research the length of driver shafts and make speculations as to why a golfer of a given height cannot use as long a shaft as they might want on their driver. Encourage interested students to investigate the role of the double-pendulum in a trebuchet, and make connections to the golf swing. The video also discusses torque, using a wrench as an illustration. When tightening a bolt to specifications, it is necessary to know how much torque (measured in foot-pounds or newton-meters) a wrench is exerting. “Torque wrenches” indicate the amount of torque applied in some way – with symbols on older models, but now digitally. Have students research digital torque wrenches, both to find how they work and also their real-world uses. (page 2) Connect to Engineering The engineering design process involves identifying problems and finding solutions, usually as part of an ongoing cycle of innovation. The video discusses centripetal force. An interesting device that uses this concept – sometimes described in terms of its “fictitious force” counterpart, centrifugal force – is the “governor.” This device uses negative feedback to regulate fuel or steam flow in engines, for example. Take Action with Students Ask students to research the history and use of “centrifugal governors.” Have students brainstorm to see if they can think of any other devices that might use this “centrifugal” effect. Connect to Math Centripetal force is described by a mathematical equation, Fc = mv2/r, where m is the mass of the object, v is its speed, and r is the radius of the circular path it is taking. Three relationships are contained in this expression: a direct proportion between Fc and m, and inverse proportion between Fc and r, and a direct proportion between Fc and the square of v. Take Action with Students Have students reason about what would happen to the centripetal force on an object going in a circle if the mass were tripled, cut in half, etc., while holding speed and radius constant. You might use specific numbers – for example, say the tension in a string holding on to a whirling 0.5 kg potato is 3 newtons. What would the tension be if the potato’s mass were suddenly changed to 1.5 kg? (Answer = 9 newtons) Have students reason about what would happen to the centripetal force on an object going in a circle if the radius were tripled, cut in half, etc., while holding mass and speed constant. You might use specific numbers – for example, say the radius of the circle is 0.4 meters and the tension in the string is 3 newtons. What would the tension be if the radius were suddenly changed to 1.2 meters? (Answer = 1 newton) Have students reason about what would happen to the centripetal force on an object going in a circle if the speed were tripled, cut in half, etc., while holding mass and radius constant. You might use specific numbers – for example, say the speed is 0.6 meters per second and the tension in the string is 3 newtons. What would the tension be if the speed were suddenly changed to 1.8 meters per second? (Answer = 27 newtons) (page 3) Facilitate SCIENCE Inquiry 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 11. Explore Understanding Students may consider the question of how energy is transferred from one object to another in the most efficient way, so as to maximize the kinetic energy – and therefore speed – of the second object. Guide students to think about how players who use an “extension” – such as a tennis racket, baseball bat, or golf club – can maximize the energy transferred from their bodies to the object they are trying to advance. Examples of pendulums in sports are.... In the sport of _____, one goal is to transfer energy from the athlete to _____ by.... Maximizing the energy transferred involves not only strength but also.... A [tennis, baseball, golf] swing is more productive, or “better,” when.... Show the video Science of Golf: Physics of the Golf Swing. Continue the discussion of the transfer of energy during a golf swing with prompts such as these: When I watched the video, I thought about.... Torque is important in a golf swing because.... The pivot point(s) about which torque is applied is (are).... Centripetal force is important in a golf swing because.... The centripetal force is applied by.... The double pendulum is important in a golf swing because.... The two parts of the double pendulum in a golf swing are.... Ask Beginning Questions Stimulate small-group discussion with the prompt: This video makes me think about these questions.... Then have groups list questions they have about the double pendulum and centripetal force. Ask groups to choose one question and phrase it in such a way as to be researchable and/or testable. The following are some examples. What is the double pendulum and how does it act as a system? Does the double pendulum effect increase club head speed relative to a single pendulum of the same length? What is the angle between the two legs of the double pendulum when club head speed is at a maximum? How much different would club head speed be if no torque were applied at the joint between the two legs of the pendulum (i.e., at the wrists)? How much of the club head’s kinetic energy can be attributed to lost gravitational potential energy? (page 4) Design Investigations 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. Possible Materials Allow time for students to examine and manipulate the materials available. Doing so often aids students in refining their questions or prompts new ones that should be recorded for future investigation. In this inquiry, students might use materials such as a golf ball (a real one, a foam practice ball, or both); a pair of meter (or half-meter) sticks each with holes drilled near each end; a bolt which just fits into the drilled holes, nuts to go with the bolt, a small wooden block, and a table top. For example, a double pendulum might be made of two half-meter sticks – each with two holes, one at either end of the stick, drilled about 5 centimeters from the ends. The meter sticks could be joined by placing a bolt through one set of holes. With the nut on the bolt loosely, the stick will be able to pivot to make a double pendulum. With the bolt very tight, the two should swing as a unit. Another bolt can be used at the end of one stick to be the overall pivot point, and the other end could be used to attach a wooden block, to serve as the club head. Optionally, an identical block could be attached to the center of the upper arm, so that the two legs have the same mass. It could be interesting to let the students video themselves making golf swings. This could help them see how differently they move, and make more direct connections to the video and the concepts under study. A golf pro from a local country club might be invited to come in for demonstrations and discussions. Safety Considerations To augment your own safety procedures, see NSTA’s Safety Portal at http://www.nsta.org/portals/safety.aspx. Open Choice Approach (Copy Master page 11) Groups might come together to agree on one question for which they will explore an answer, or each group might explore something different. Students should brainstorm to form a plan they would have to follow in order to answer the question, which might include researching background information. Work with students to develop safe procedures that control variables and enable them to gather valid data. Encourage students with prompts such as the following: Information we need to understand before we can start our investigation is.... We might create a different swing method to maximize the torque by.... We might investigate the effect of the double pendulum’s length on distance by.... The variables we will be manipulating will be.... Our hypothesis is that.... To test our hypothesis, we will.... To conduct the investigation safely, we will.... (page 5) Focused Approach (Copy Master pages 12–13) The following exemplifies how students might engineer a method for hitting a golf ball with a gravitationally-driven double-pendulum club, and testing to compare ball speed resulting from a strike with a double-pendulum club as opposed to a single-pendulum club. After students examine the materials you have available, guide them as needed to assemble a double-pendulum club that can be easily converted to a single pendulum (similar to that described in the Possible Materials section). How will we join the two legs of the pendulum? How will we make it possible to convert it to a single pendulum of the same length? How will we attach the club head? How will we support the upper pivot point, and yet have its position adjustable? If we want the two legs to have equal masses, how can we accomplish that? Students might now find the center of mass of the lower leg by balancing it (after disconnecting from the upper leg) on a pencil or something similar. The reason for doing this is so that they can control the gravitational potential energy by always releasing the center of mass from the same height. For a more accurate result, advanced students might also find the masses of both legs, so that they can use a weighted average of the centers of mass. Another option here could be to attach a block identical to that used for the club head to the middle of the upper arm, to equalize its mass so that the center of mass of the whole system is simply the average height of the two separate legs. Knowing the center of mass of this leg helps us think about.... We found the center of mass of the lower leg to be.... Equalizing the masses of the legs might be helpful because.... After developing a way to let gravity swing the club to hit the ball consistently, students might first tighten the “joint” between the legs so that it functions as simple, single, straight pendulum. They then might hold or mount it above a table, with a golf ball (actual or foam) on a tee at the end of the table, and release it from the horizontal position so that it strikes the ball, which then lands some distance out onto the floor. Students might measure the horizontal distance the ball travels before hitting the floor. Students might repeat this several times and record all the distances travelled. They might also repeat with the other type of golf ball (foam versus actual). We will hold the top pivot of the pendulum still by.... We will release the pendulum from an angle (with respect to vertical) of.... The height of the center of mass of the pendulum above the table will be.... The distance the ball landed from the table was... Students might now slightly loosen the joint so that the club functions as a double pendulum. Because we want to control for gravitational potential energy, the center of mass of the entire system should be the same as before – at the same height as the pivot point, for example. If the system is released all from a horizontal position, the angle between the two legs will change dramatically and the club head may miss the ball. For this reason, trial and error will be needed to find initial angles, with the lower (or outer) leg bent back somewhat, so that the ball can be struck. Slight adjustments of the position of the pivot point may also be needed. In all cases, the center of mass of the system should be released from the same height as for the single pendulum. Release this system (both legs simultaneously) several times to strike the ball, each time recording the distance the ball lands from the table. Repeat, using the other ball. Through trial and error, we found the angle for the upper (inner) arm relative to the vertical must be.... Through trial and error, we found the angle between the arms must be.... The distance the ball landed from the table was... The single (double) pendulum hit caused the ball to go further because.... The reason we were careful to equalize the height of the center of mass is.... (page 6) Media Research Option Groups might have questions that are best explored using print media and online resources, such as those relating to why swings work or don’t work or how swings vary among players (while still exhibiting the double pendulum). 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 effort 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 the investigation safely, we will.... Make a Claim Backed by Evidence Students should analyze their data and then make one or more claims based on the evidence their data shows. Encourage students with this prompt: As evidenced by... we claim... because.... An example claim might be: As evidenced by the greater distance traveled by the ball struck by the double pendulum, we claim that it is more productive than hitting the ball with a single pendulum because the second pendulum accelerated more rapidly and thus hits the ball with more force. Compare Findings Encourage students to compare their ideas with others, such as classmates who investigated a similar (or different) question or system, or to compare their ideas with material they found on the Internet, in their textbooks, or heard from an expert they chose to interview. Remind students to credit their original sources in their comparisons. Elicit comparisons from students with prompts such as the following: My ideas are similar to (or different from) those of the experts in the video in that.... My ideas are similar to (or different from) those of my classmates in that.... My ideas are similar to (or different from) those that I found on the Internet in that.... Students might make comparisons like the following: A major difference between our club and the situations in the video is that, in the video, the golfers were able to apply a significant torque to both arms of the double pendulum, rather than relying on gravity alone. (page 7) Reflect on Learning Students should reflect on their understanding, thinking about how their ideas have changed or what they know now that they didn’t know before. Encourage reflection, using prompts such as the following: The claim made by the expert in the video is.... I support or refute the expert’s claim because in my investigation.... When thinking about the expert’s claims, I am confused as to why.... Another investigation I would like to explore is.... Inquiry Assessment See the rubric included in the student Copy Masters on page 14. Incorporate Video into Your Lesson Plan Integrate Video in Instruction Real World Connections Torque, like force, causes a change in motion – in particular, rotational motion. Torque is important for many applications other than golf swings. Many types of motors use rotating shafts as their output mechanisms. Automobile engines are a good example, and the amount of torque produced at different rotational speeds (measured in revolutions per minute) is widely used to characterize their performance. Graphs showing this information are commonly used, and the area underneath the curve shows the power output of the engine. Have students research torque as it applies to automobile engine performance, noting the units and the relationship to power. Students might also make calculations using the concept of torque as force times lever arm, to calculate how long of a lever arm it would take for a student’s weight to fully counteract the maximum torque provided by a typical automobile engine (i.e., if the student were standing on a long wrench, with the engine trying to pick up the student). Compare and Contrast The video discusses centripetal force, but a perhaps more commonly heard term is centrifugal force. Generally, physicists regard centripetal force as real and centrifugal force as fictitious (or using other descriptors, such as pseudo). In some cases, physicists may use centrifugal force for convenience, understanding that it seems to exist only in an accelerated reference frame (i.e., a rotating one). Centrifugal force can also be used to refer to the equal and opposite reaction to a centripetal force. Have students research these terms, including the etymology of the words, and clearly explain how the terms are similar and how they are different. As an extension, students might search for examples of other inertial forces, such as the Coriolis force, and describe situations in which these apparent forces might be experienced. Students might even debate whether or not these inertial forces should be regarded as real, and whether or not they are useful (real or not). (page 8) Using the 5E Approach? If you use a 5E approach to lesson plans, consider incorporating video in these Es: Explain: In the video, the claim is made that when the club swings in a wider (larger radius) arc, less centripetal force is required. This is true as long as the mass and the speed are held constant, though it is not true if the angular speed (i.e., measured in revolutions per minute) is held constant. Have students use the formula Fc = mv2/r to show how a larger radius makes a smaller force. Have students try to explain in common sense terms (rather than just by appealing to the formula) why this should be true. Have them brainstorm to come up with examples of this relationship – for example, a car going around a wider turn at a given speed is less likely to skid off the road. Elaborate: In the video, many slow-motion phantom camera shots show the golf swing in action. 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 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. Connect to ... Biomechanics The golf swing is an excellent application of biomechanics, which employs engineering to analyze biological systems. Have students research biomechanics in general, and the biomechanics of the golf swing in particular. Ask them to explain the roles of torque, centripetal force, and the double pendulum in greater detail, using posters or slide shows. Connect to ... Physical Education In some ways, a golf swing is similar to certain moves (i.e., kicks) used in various martial arts. Like the golfer trying to transfer and concentrate energy from a large number of the body’s muscles into a club head, a practitioner of martial arts tries to concentrate such energy into a particular body part (i.e., a foot). Some of the same concepts used in the video may apply here. Have students research the physics of selected martial arts moves (like a roundhouse kick) to find similarities to and/or differences from the golf swing. Students could use video cameras to record themselves in action, and then view the video frame-by-frame to analyze exactly how they are moving. Use Video as a Writing Prompt Have students watch the video once or twice, taking notes on the meanings of the three physics concepts highlighted in the video. After this, students might express in writing their understanding of the meaning of these concepts, including at least one example of how each concept applies to the golf swing, and at least one example of an application of these concepts outside of golf. (page 9) COPY MASTER: Open Choice Inquiry Guide for Students Science of Golf: Physics of the Golf Swing Use this guide to investigate a question about the role(s) of torque, centripetal force, and/or the double pendulum in an action. Write your lab report in your science notebook. Ask Beginning Questions The video makes me think about these questions.... Design Investigations Choose one question. How can you answer it? Brainstorm with your teammates. Write a procedure that controls variables and makes accurate measurements. Look up information as needed. Add safety precautions. Use these prompts to help you design your investigation. Information we need to understand before we can start our investigation is.... We will construct any equipment needed by.... The procedure to be used with our equipment is.... The variables we will be measuring are.... The hypothesis we will be testing is.... To conduct the investigation safely, we will.... Record Data and Observations Record your observations. Organize your data in tables or graphs as appropriate. Make a Claim Backed by Evidence Analyze your data and then make one or more claims based on the evidence your data show. Make sure that the claim goes beyond summarizing the relationship between the variables. My Evidence My Claim My Reason Compare Findings Review the video and then discuss your results with classmates who investigated the same or a similar question. Or do research on the Internet or talk with an expert. How do your findings compare? Be sure to give credit to others when you use their findings in your comparisons. My ideas are similar to (or different from) those of the experts in the video in that.... My ideas are similar to (or different from) those of my classmates in that.... My ideas are similar to (or different from) those that I found on the Internet in that.... Reflect on Learning Think about what you found out. How does it fit with what you already knew? How does it change what you thought you knew? The claim made by the expert in the video is.... I support or refute the expert’s claim because in my investigation.... When thinking about the expert’s claims, I am confused as to why.... Another investigation I would like to explore is.... (page 10) COPY MASTER: Focused Inquiry Guide for Students Science of Golf: Physics of the Golf Swing Use this guide to investigate how effectively energy is transferred from its potential to kinetic form in the cases of single and double pendulums used to strike a golf ball. Write your lab report in your science notebook. Ask Beginning Questions How can we compare double-pendulum and single-pendulum golf swings in terms of resulting ball speed? Design Investigations Brainstorm with your teammates about how to answer the question. Write a procedure that controls variables and allows you to gather valid data. Add safety precautions as needed. Use these prompts to help you design your investigation. We will raise the center of mass of the club to an angle or height of.... The center of mass of the club will fall a distance of.... With the double-pendulum version, we will vary.... We will compare the speeds of the golf ball by.... To conduct the investigation safely, I need to.... Record Data and Observations Organize your observations. Organize your data in tables or graphs as appropriate, using the following as examples. Be sure to record the location of the center of mass if needed. Distances Traveled for Different Initial Configurations Pendulum style Angle between upper arm and vertical Angle between upper arm and lower arm Height of center of mass above table (to be held constant) Distance ball traveled horizontally Single, trial 1 Single, trial 2 Single, trial 3 Double, trial 1 Double, trial 2 Double, trial 3 (page 11) Ideas for Analyzing Data On average, how far did the ball land from the edge of the table when it was struck by the single pendulum? What combination of angles with the double pendulum successfully struck the ball and made it go the greatest distance? On average, how far was this? How did the distance traveled using the optimal double pendulum compare to that using the single pendulum? What explanation might you have for any differences between the distances resulting from the single and double pendulums? What are some sources of error in our methods, and how could our accuracy be improved? Make a Claim Backed by Evidence Analyze your data and then make one or more claims based on the evidence shown by your data. Make sure that the claim goes beyond summarizing the relationship between the variables. My Evidence My Claim My Reason Compare Findings Review the video and then discuss your results with classmates who did the investigation using the same or a similar system or with those who did the investigation using a different system. Or do research on the Internet or talk with an expert. How do your findings compare? Be sure to give credit to others when you use their findings in your comparisons. My ideas are similar to (or different from) those of the experts in the video in that.... My ideas are similar to (or different from) those of my classmates in that.... My ideas are similar to (or different from) those that I found on the Internet in that.... Reflect on Learning Think about what you found out. How does it fit with what you already knew? How does it change what you thought you knew? The claim made by the expert in the video is.... I support (or refute) the expert’s claim because in my investigation.... When thinking about the expert’s claims, I am confused as to why.... Another investigation I would like to explore is.... (page 12) COPY MASTER: Assessment Rubric for Inquiry Investigations Criteria 1 point 2 points 3 points Initial question Question had a yes/no answer, was off topic, or otherwise was not researchable or testable. Question was researchable or testable but too broad or not answerable by the chosen investigation. Question clearly stated, 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. While the design supported the initial question, the procedure used to collect data (e.g., number of trials, control of variables) was not sufficient. Variables were clearly identified and controlled as needed with steps and trials that resulted in data that could be used to answer the question. Variables 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 results in data that 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. Observations and data Observations were not made or recorded, and data are unreasonable in nature, not recorded, 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 question. 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 reflections were limited to a description of the procedure used. Student reflections were not related to the initial question. Student reflections described at least one impact on thinking. Lesson plans produced by the National Science Teachers Association. Video produced by NBC News Learn in collaboration with the National Science Foundation. sports in this article Golf tags in this article Athlete Fan NBC News Learn Science of Golf