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AP PHYSICS 1 (SECONDARY) ESSENTIAL UNIT (E07) (Rotational Motion & Torque) (Giancoli Chapter 8) (July 2015) Unit Statement: Until now, only translational motion has been discussed, namely; kinematics, dynamics and the role that force and energy have on this type of motion. This unit will focus on rotational motion including torque and the affect energy, angular momentum and force have on rotational motion. This unit will significantly help in the understanding of the world around us from rotating bicycle wheels, how DVD’s play, to amusement park rides, planet rotation and centrifuges. All of the information mastered in the last units will be reiterated and used for further investigations. (Estimated class time three weeks) Essential Outcomes: (must be assessed for mastery) 1. The Student Will describe the force component as being perpendicular to the line connecting the axis of rotation and the point of application of the force resulting in a torque about that axis. Including: a. The lever arm is the perpendicular distance from the axis of rotation or revolution to the line of application of the force. b. The magnitude of the torque is the product of the magnitude of the lever arm and the magnitude of the force. c. The net torque on a balanced system is zero. (EK 3.F.1) 2. TSW predict the behavior of rotational collision situations, by the same processes that are used to analyze linear collision situations, using an analogy between impulse and change of linear momentum and angular impulse, and change of angular momentum. (LO 3.F.3.1) 3. TSW justifies that a torque exerted on an object can change the angular momentum of an object. (EK 3.F.3) 4. TSW will recognize the presence of a net torque along any axis causes a rigid system to change its rotational motion or an object to change its rotational motion about that axis. Including: a. Rotational motion can be described in terms of angular displacement, angular velocity, and angular acceleration about a fixed axis. b. Rotational motion of a point can be related to linear motion of the point using the distance of the point from the axis of rotation. c. The angular acceleration of an object or rigid system can be calculated from the net torque and the rotational inertia of the object or rigid system. (EK3.F.2) 64 QSI AP PHYSICS 1 SEC E07 Copyright © 1988-2015 5. TSW characterize torque, angular velocity, angular acceleration, and angular momentum as vectors and classify as positive or negative depending upon whether they give rise to or correspond to counterclockwise or clockwise rotation with respect to an axis. (EK 4.D.1) 6. TSW calculate the change in angular momentum given by the product of the average torque and the time interval during which the torque is exerted. (EK 4.D.3) 7. TSW justify that if the net external torque exerted on the system is zero, the angular momentum of the system does not change. (EK 5.E.1) 8. TSW describe or calculate the angular momentum and rotational inertia of a system in terms of the locations and velocities of objects that make up the system. (LO 5.E.2.1) Guided or Essential Questions: 1. What are the conditions necessary for two people with significant differences in mass to balance on a seesaw? 2. What are the conditions necessary for static equilibrium? 3. In what ways are rotational motion and linear motion related? 4. What are the relationships among angular momentum, angular velocity, angular acceleration, rotational inertia, and torque? Key Concepts: Rigid Object Axis of rotation Instantaneous angular velocity Frequency Constant angular acceleration Lever arm (moment arm) Rotational Kinetic Energy Law of conservation of angular momentum 65 QSI AP PHYSICS 1 SEC E07 Copyright © 1988-2015 Radian Average angular velocity Instantaneous angular acceleration Period Torque Moment of inertia Angular momentum Right-hand rule Some Common Equations for this Unit: t t vT r aT r Angular Velocity Angular Acceleration Tangential velocity Tangential acceleration Centripetal acceleration vT2 r 2 r 1 it (t ) 2 2 f i t f 2 i 2 2 1 KEr I 2 2 ac v Uniformly accelerated rotational motion Rotational kinetic energy 2r T Velocity of a satellite in circular orbit, with period T Centripetal force on an orbiting satellite mv 2 Fc r v T Velocity of a satellite in circular orbit GmE r 2r Period of a satellite in circular orbit 3 2 GmE FL sin Torque I mL2 Moment of inertia 66 QSI AP PHYSICS 1 SEC E07 Copyright © 1988-2015 Schedule of suggested laboratory experiments (guided inquiry format is suggested for labs shaded in gray) TSW # Lab # 1 33 Name of Laboratory Balancing Act Description of Lab In this activity, students work in groups to discover the relationship between force and torque. Students are given hooked masses and a meterstick with predrilled holes, and they must create as many different configurations as they can that balance the stick horizontally. Then students calculate the torques produced (clockwise and counterclockwise) in each configuration. Follow-up questions include the following: 1. Does the angle at which a force is applied affect the total torque? 2. You are stranded in a situation where you need to loosen a rusty bolt. You have a wrench, but using it you are still unable to apply enough torque to loosen the bolt. You also have some pieces of steel pipe. How can you loosen the bolt without much effort? Associated Science Practices 1.1, 1.2, 1.4, 1.5, 2.1, 2.2, 3.1, 4.1, 4.2, 4.3, 5.1, 5.3, 6.1, 6.4, 7.2 Teacher Produced Or PhET Balancing Act could be used instead (see link below) 2 3, 4, 5 34 35 “Lady Bug: Angular Kinematics” and “Ladybug Revolution” Merry Go Round “Lady Bug: Angular Kinematics,” a guided-inquiry activity that involves the “Ladybug Revolution” simulation, is used to help students discover the basics of rotational kinematics. Angular velocity, angular acceleration, and the relationships of the angular kinematic equations to their linear counterparts are investigated. Answers to questions embedded within the activity are submitted for grading, and student–teacher discussions are held as needed to address student misconceptions. PhET- see link below Working in small groups, students use a playground merry-go-round to investigate how the application of an external torque affects the angular velocity and angular momentum of an object. Once students believe they have a qualitative idea of the relationship, they must collect and analyze data to support their conclusions quantitatively. A lab report is required from each group at the conclusion of the activity. Teacher Option 1.http://hendrix2.uoregon.edu/~dlivelyb/phys101/lab4_s 07.pdf 2.http://dev.physicslab.org/Document.aspx?doctype=3&f ilename=RotaryMotion_CentripetalAccRotation.xml 3.http://www.dartmouth.edu/~physics/labs/writeups/ro tational.motion.pdf 67 QSI AP PHYSICS 1 SEC E07 Copyright © 1988-2015 1.1, 1.2, 1.4, 1.5, 2.1, 2.2, 3.1, 4.1, 4.2, 4.3, 5.1, 5.3, 6.1, 6.4, 7.2 1.1, 1.2, 1.4, 1.5, 2.1, 2.2, 3.1, 4.1, 4.2, 4.3, 5.1, 5.3, 6.1, 6.4, 7.2 1,4 1-5 36 37 Popper toy, circular rotating Platforms Conservation of Angular Momentum and Energy Working in groups, students analyze and predict the motion of two adjacent merry-go-round analogs when a popper toy is used to exert a force from one onto the other in two situations: 1. From the bottom of the left-hand merry-goround to the bottom of the right-hand merrygo-round (viewed from above)Along a line tangent to the circles, from one onto the other, where the adjacent merry-go-rounds touch 2. Students should easily determine the expected direction of rotation for both merry-go-rounds after the forces are applied, but they should find an apparent discrepant event in terms of conservation of angular momentum. Group members conduct research and collaborate to determine why the law of conservation of angular momentum is not broken. Each group provides a written explanation. WebQuest In pairs or small groups, students investigate how the angular momentum of a rotating system responds to changes in the rotational inertia. The experiment involves the collection of data of angle versus time and angular velocity versus time. Students use a rotary motion sensor with an aluminum plate that is spun to a certain angular speed, and then a second plate is dropped onto the first one, resulting in a change of the moment of inertia and the angular speed. The students analyze the graphs before and after the changes in the rotational inertia and determine the effect of changes in the rotational inertia on the angular momentum of the system. 1.1, 1.2, 1.4, 1.5, 2.1, 2.2, 3.1, 4.1, 4.2, 4.3, 5.3, 6.1, 6.4, 7.2 1.1, 1.2, 1.4, 1.5, 2.1, 2.2, 3.1, 4.1, 4.2, 4.3, 5.1, 5.3, 6.1, 6.4, 7.2 Vernier Suggested Materials: 1. Giancoli, D.C. Physics: Principles with Applications. Englewood Cliffs, NJ: Pearson Education. 2. Appel, K, Ballen, C, Gastineau, J, Vernier, D. Physics with Vernier. Beaverton, OR; Vernier Software and Technology, 2010. 3. Puri, O; Zober, P. Physics. A laboratory manual; Boston, Mass. N.Y: Pearson Custom Pub., 2002. 8th edition 4. Optional- Van Hook, Stephen J. “Battle of the Merry-Go-Rounds: An Angular Momentum Demonstration.” The Physics Teacher 44, no. 5 (2006): 304-307. http://scitation.aip.org/content/aapt/journal/tpt/44/5/10.1119/1.2195403 Suggested Technology Resources: Labs, in class activities, quizzes, videos and demos: 1. Quick Podcast explaining equilibrium by drawings so everyone can understand the topic. This is the first in a series. Hewitt-Drew-it! PHYSICS 1. Equilibrium Rule Hewitt-Drew-it!https://www.youtube.com/watch?v=t0akAKlJ3nc&safe=active 2. A figure skater, and Dartmouth student, demonstrates the conservation of angular momentum. https://www.youtube.com/watch?v=VmeM0BNnGR0 68 QSI AP PHYSICS 1 SEC E07 Copyright © 1988-2015 3. More on figure skating and physics- http://www.bsharp.org/physics/spins 4. Notes on Kepler’s Laws- http://www.nuffieldfoundation.org/node/1785 5. Calculating Torques Online Activity- In this activity we learn to calculate the torque caused by a force. http://media.pearsoncmg.com/bc/aw_young_physics_11/pt1a/Media/RotMotionStatics/Calcul atingTorques/Main.html 6. Ball hits Bat- Angular Momentum Online Activityhttp://media.pearsoncmg.com/bc/aw_young_physics_11/pt1a/Media/RotMotionStatics/BallH itsBat/Main.html 7. Armed Levers- In this activity, we use the principles of statics to analyze the biceps and the triceps muscle systems of the arm. http://media.pearsoncmg.com/bc/aw_young_physics_11/pt1a/Media/RotMotionStatics/ArmL evers/Main.html 8. Interactive Circular Motion Tutorialhttp://www.mhhe.com/physsci/physical/giambattista/circular/circular.html 9. Circus Physics: Conservation of Angular Momentum. http://video.pbs.org/video/1607951704/ 10. Rotational Kinematics Online Lab Activityhttp://dev.physicslab.org/Document.aspx?doctype=3&filename=RotaryMotion_RotationalKi nematics.xml 11. Online Notes about Forces and Torques in Muscles and Jointshttp://cnx.org/contents/[email protected]:66/College_Physics 12. PhET- Balancing Act- Seesaw Interactive labhttp://phet.colorado.edu/en/simulation/balancing-act 13. PhET- Lady Bug Angular Kinematics- http://phet.colorado.edu/en/contributions/view/3020 14. PhET- Lady Bug Revolution- http://phet.colorado.edu/en/simulation/rotation Note- All links to online resources were verified before publication. In cases where links are no longer working, we suggest that you try to find the resource by a keyword internet search. RUBRIC FOUND ON FOLLOWING PAGE……………………………………… 69 QSI AP PHYSICS 1 SEC E07 Copyright © 1988-2015 SUGGESTED RUBRIC AP PHYSICS 1 E07 Student Name: __________________________ Date: _______________________ To receive a ‘B’, the student must show ‘B’ level mastery on all essential outcomes (TSW’s). The teacher’s discretion on the student’s holistic performance on the unit, including such items as: the above ‘A’ level rubric, the unit project, group work and class discussions will determine ‘A’ level mastery. If grading for AP test preparation, please refer to Course Outcome Rubric. The Student Will 1. TSW describe the force component as being perpendicular to the line connecting the axis of rotation and the point of application of the force results in a torque about that axis. Including: a. The lever arm is the perpendicular distance from the axis of rotation or revolution to the line of application of the force. b. The magnitude of the torque is the product of the magnitude of the lever arm and the magnitude of the force. c. c. The net torque on a balanced system is zero. (EK 3.F.1) 2. TSW predict the behavior of rotational collision situations by the same processes that are used to analyze linear collision situations using an analogy between impulse and change of linear momentum and angular impulse and change of angular momentum. (LO 3.F.3.1) ‘A’* LEVEL Calculates torques on a two-dimensional system in static equilibrium, by examining a representation or model (such as a diagram or physical construction). (LO 3.F.5) 3. TSW justifies that a torque exerted on an object can change the angular momentum of an object. (EK 3.F.3) Plans data collection and analysis strategies designed to test the relationship between torques exerted on an object and the change in angular momentum of that object. (LO 3.F.3.3) 4. TSW will recognize the presence of a net torque along any axis will cause a rigid system to change its rotational motion or an object to change its rotational motion about that axis. Including: Plans data collection and analysis strategies designed to test the relationship between a torque exerted on an object and the change in angular velocity of that object about an axis. (EK3.F.2.2) Or Designs an experiment and analyzes data testing a question about torques in a balanced rigid system. (LO 3.F.4) Appropriate concepts that are fully understood (right hand rule, perpendicular distance angular inertia, etc.) clearly stated and employed correctly. 70 QSI AP PHYSICS 1 SEC E07 Copyright © 1988-2015 ‘B’ LEVEL Uses representations to compare and estimate the torques on an object caused by various forces. (LO 3.F.1 and LO 3.F.1.2) In an unfamiliar context or using representations beyond equations, the student is able to justify the selection of a mathematical routine to solve for the change in angular momentum of an object caused by torques exerted on the object. (LO 3.F.3.2) Makes predictions about the change in the angular velocity about an axis for an object when forces exerted on the object cause a torque about that axis. (EK3.F.2.1) Comments a. Rotational motion can be described in terms of angular displacement, angular velocity, and angular acceleration about a fixed axis. b. Rotational motion of a point can be related to linear motion of the point using the distance of the point from the axis of rotation. c. The angular acceleration of an object or rigid system can be calculated from the net torque and the rotational inertia of the object or rigid system. (EK3.F.2) 5. TSW characterize torque, angular velocity, angular acceleration, and angular momentum as vectors and as positive or negative depending upon whether they give rise to or correspond to counterclockwise or clockwise rotation with respect to an axis. (EK 4.D.1) 6. TSW calculate the change in angular momentum given by the product of the average torque and the time interval during which the torque is exerted. (EK 4.D.3) 7. TSW justify that if the net external torque exerted on the system is zero, the angular momentum of the system does not change. (EK 5.E.1) Plans data collection strategies designed to establish that torque, angular velocity, angular acceleration, and angular momentum can be predicted accurately when the variables are treated as being clockwise or counterclockwise with respect to a well-defined axis of rotation, and refine the research question based on the examination of data. (LO 4.D.1.2 ) Plans a data collection strategy designed to test the relationship between the change in angular momentum of a system and the product of the average torque applied to the system and the time interval during which the torque is exerted. (LO 4.D.3.2) Describes a representation and use it to analyze a situation in which several forces exerted on a rotating system of rigidly connected objects change the angular velocity and angular momentum of the system. (LO 4.D.1.1 ) Makes calculations of quantities related to the angular momentum of a system when the net external torque on the system is zero. (LO 5.E.1.2) Makes qualitative predictions and justifications about the angular momentum of a system for a situation in which there is no net external torque. (LO 5.E.1.1) 8. TSW describe or calculate the angular momentum and rotational inertia of a system in terms of the locations and velocities of objects that make up the system. (LO 5.E.2.1) Approach and starting equations chosen are clearly shown, clearly written & all elements are valid. Students are expected to do qualitative reasoning with compound objects. Students are expected to do calculations with a fixed set of extended objects and point masses. 71 QSI AP PHYSICS 1 SEC E07 Copyright © 1988-2015 Uses appropriate mathematical routines to calculate values for initial or final angular momentum, or change in angular momentum of a system, and/or average torque or time during which the torque is exerted in analyzing a situation involving torque and angular momentum. (LO 4.D.3.1)