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
1.2.1
4
5
6
7
4.2.1
8
8.2.1
8.3.2
History & Process Standards
K
1
2
3
4
5
6
7
8
Skills Used/Developed:
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Thermal Conductivity - V 2.0 ©Copyright University of Nebraska 1997
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
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Thermal Conductivity - V 2.0 ©Copyright University of Nebraska 1997
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
IV. LIST OF MATERIALS
“where’s the handle”
clamp
hanging thing from broom handle
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.
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Thermal Conductivity - V 2.0 ©Copyright University of Nebraska 1997
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.
(force1)(distance1)=(force2)(distance2)
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 50N-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.
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Thermal Conductivity - V 2.0 ©Copyright University of Nebraska 1997
VII. FREQUENTLY ASKED QUESTIONS
VIII. TROUBLE SHOOTING
IX. HANDOUT MASTERS
X. REFERENCES
Physics Algebra/Trig by Eugene Hecht
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Thermal Conductivity - V 2.0 ©Copyright University of Nebraska 1997