TORQUE Diandra Leslie-Pelecky Edited by Anne Starace Abstract: As you may have noticed, it is much more difficult to hold an object at arm s length than close to your body and door handles are placed on the opposite side of doors hinges. Both these occurrences are explained in this module using the concept of torque. Keywords: Mechanics; Newton's Second Law; Rotational Dynamics; Force; Torque; Angular Acceleration Funded by the National Science Foundation and the University of Nebraska
Content Standards K 1 2 3 4 5 6 7 8 1.2.1 4.2.1 8.2.1 8.3.2 History & Process Standards K 1 2 3 4 5 6 7 8 Skills Used/Developed: 2
TABLE OF CONTENTS I. OBJECTIVES...4 II. SAFETY...4 III. LEVEL, TIME REQUIRED AND NUMBER OF PARTICIPANTS...4 IV. LIST OF MATERIALS...4 V. INTRODUCTION...4 VI. PROCEDURE...5 VII. FREQUENTLY ASKED QUESTIONS...6 VIII. TROUBLE SHOOTING...6 IX. HANDOUT MASTERS...6 X. REFERENCES:...6 3
I. OBJECTIVES Students will: -understand the concept of torque -learn how torque is mathematically calculated. II. SAFETY Watch the hinges around the students! When the board falls, it falls hard, so make sure the students stand back. III. LEVEL, TIME REQUIRED AND NUMBER OF PARTICIPANTS LEVEL The activity is appropriate for all ages. TIME REQURED 5-15 minutes NUMBER OF PARTICIPANTS Groups of 4-6 are optimal, but larger groups can also be handled where s the handle clamp hanging thing from broom handle IV. LIST OF MATERIALS newton meter broom handle multicolored weight set V. INTRODUCTION Torque is the cross product of the leaver arm and the force vector, T=r x F or, in other words, the length between the point of rotation and the force, multiplied by the magnitude of the force, multiplied by the sin of the angle in between them: T=rFsin(θ) Note that a bolded variable is a vector. 4
Also, torque equals angular acceleration, α, multiplied by the moment of inertia, I, of the object rotating: T=Iα The moment of inertia is a number which tells us how easy it is to get an object rotating. So, if you are using the same object, I is a constant. If I is a constant, then torque must be proportional to angular acceleration. When you are doing something like holding a broom horizontally or opening a door, the angular acceleration will probably be constant. So if I is constant and α is constant, then torque must be constant. So, remembering that T = r x F, when you push on a different place on the door, r changes, so in order to keep T constant, the force must change too. If something is balanced on a fulcrum the net torque must be zero. In other words, the force multiplied by the distance from the fulcrum must be equal on both sides of the fulcrum. (force 1 )(distance 1 ) = (force 2 )(distance 2 ) A seesaw is a good example of this. If a 100 lbs pound person is sitting on one side of the seesaw and a 50 pound person is sitting on the other, the seesaw will balance if the 100lbs person is sitting one foot away from the center and the 50lbs person is sitting two feet away from the center. (100)(1)=(50)(2) VI. PROCEEDURE BIG TORQUE Hold the end of a broom handle in one hand and extend your arm and the broom handle horizontally in front of you. Tie a string around an object and hang the object under the stick a few centimeters from your hand. Try to keep the stick horizontal while someone slides the object toward the end of the stick. As the object is pushed farther from you, you will notice that it is increasingly difficult to hold the broom horizontally. The weight of the stick and object do not change, but the position of the object changes. This changes the position of the force vector and lever arm so that the torque increases. WHERE S THE HANDLE? This demo shows why door handles are located opposite the hinges. Set the board on the ground or use the c-clamp to clamp the board to a table. There are three different knobs to open this door. Ask the students which one they think would be easiest to use to open the door. Let the students try to lift the board by using each of the three handles. They will find that the board gets easier to lift as you get farther from the hinge. To prove all this in no uncertain terms, use the Newton Meter to demonstrate that the force needed to lift the board to the same height, increases as the handle is moved closer to the hinge. Don t use the 50- N-m on the innermost handle as it will break the meter! Make sure that they are pulling straight up and not at an angle if they are inconsistent, they won t feel a difference. Balancing peg board section could be added here. 5
VII. FREQUENTLY ASKED QUESTIONS VIII. TROUBLE SHOOTING IX. HANDOUT MASTERS X. REFERENCES Physics Algebra/Trig by Eugene Hecht 6