Elliot J. Michel

June 28, 2011

TIE 535 Hansen

Gagne’s Events

Topic: Introduction to torque

Target Group: 11th and 12th grade physics students

1. Gain Attention

        Invite two student participants to attempt to open the classroom door, while the rest of the class observes in pairs.  Have one student push on the outside of the unlatched door (close to the handle), then have the other push on the inside of the door (close to the hinge).  Have the class share observations with partner.  Have two volunteers narrate their experiences (the student pushing close to the hinge should have had a harder time opening the door) and ask if that is what the rest of the class noticed.

2. Establish Purpose

        Explain that students will be learning about torque

• Definition of torque
• Factors affecting torque
• Equation for torque
• Calculations of torque

3. Stimulate Recall of Prior Knowledge

        Explain to students that they will be given a basic, working definition of torque, then they will be asked to brainstorm some of the factors they think might affect torque, and they will be given a chance to play with an applet that will allow them to vary those factors.  This will be a virtual lab in which they will take data, and determine an equation governing torque.  Once an equation has been established, the class will practice performing calculations using that equation.

4. Present Content

        Working definition of torque: torque is the rotational analogue of force, that is, while a force is used to move an object in a straight path, a torque is used to turn or spin an object.  This video may help: http://www.youtube.com/watch?v=N8vwqUl4v6E

        Explain that the door opened more easily when pushed nearer to the handle because a greater torque was applied in that situation.  Have students brainstorm (on their own paper) what they factors they think will affect torque.  Have students share and record their ideas on the board.  They should come up with how hard you push (magnitude of force), where along the door you push (length of lever arm), and the angle at which you push (angle between force and lever arm).  Lend assistance if they do not discover these three variables on their own.

        Once the class knows what they will be testing for, tell them that they will be doing a virtual lab to test for the affect of these three variables on torque.  Pair students up and give them the address of the applet (http://www.usna.edu/MathDept/website/courses/calc_labs/wrench/TorqueWrench.html)  before they start up their computers, make sure that each group knows how to test each variable by controlling all others and observing the effect that changing that variable has on torque (and taking data all the while).  Note: By this point in the year, they should be familiar with this.

        Allow students to experiment with the applet, record data, and analyze data.  Bring the class back together and analyze their findings.  They should easily be able to find a direct relationship between magnitude of force and torque, likewise between length of lever arm and torque.  They should also be able to describe the relationship between angle of application and torque (i.e. “When the force is perpendicular to the lever, you get the most torque and when the force is parallel to the lever, you get no force.”) but they may struggle to uncover the sinusoidal relationship between the two.  That is OK, guide them to that relationship by asking questions along the lines of “What mathematical function do we know that gives us zero at 0°, but the greatest value at 90°?”  This should eventually lead  the students to sine, which will allow you to assemble the whole equation with them: .

        Do an example problem to show how to do the math and figure out the units: if I push on the door 0.65 m from the hinges, at an angle of 12°, and with a force of 3.5 N, what is the resulting torque on the door? (0.47 Nm).  Make a point of explaining that the output of a trigonometric function has no units so the units of torque are simply Newton meters or, it you are a fan of pickup trucks, foot pounds.

5. Guided Learning

        Allow students to practice calculations on their own by giving them problems to work on, solving for each variable and, eventually, involving additional concepts (e.g. torque addition, balancing torques, incorporating multiple forces, springs, gravitational forces, center of mass).  As students work, circulate the room to monitor and answer questions.  If one student is struggling and another is excelling, pair them up.

6. Elicit Performance

        See above.  In addition, ask groups of students to define torque in their own words, identify which variables affect torque, and how they do, and to identify a situation in their own lives that is an application of torque.

7. Provide Feedback

        See above and guide students through any struggles they might be having as well as congratulating students who get it and challenging them to go further.

8. Assess Performance

        Assign homework which should include problems similar to those done in class and the writing of a script that they might use to briefly explain torque to a family member.  Students will be assessed via the following rubric:

9. Enhance Retention

        Refresh students' memory by calling on a student to share the definition of torque and another to explain how it depends on the three variables identified in class.  Share with students that tomorrow in class they will be performing torque addition, a form of vector addition, which will allow them to properly balance teeter-totters.  But in the meantime, their knowledge of torque should help them when opening doors for their crushes and using cheater bars and wrenches to tighten bolts, etc.