Unit 1: Balancing, Torque, and Stability
Lesson 2: Defining Torque
I. Go over the results of the Balancing Acts activity
A. Go through each problem, discussing the teams answers.
B. Focusing on Problem 6 and 7, have students discuss how they came up with
their models and if their models predict whether or not the system will balance.
C. Make sure that the students understand that at each location (distance from the
pivot point) the number of paperclips is multiplied by how far it is from the pivot
point (ex. 2 paperclips at position 3 is equal to 6. All of the products on one side
of the pivot point are added together. When the sum of all the products on each
side is equal, then the system is in balance.
D. We can see that the system on the front does indeed balance, using the model.
II. Second condition for equilibrium
A. We have already gone over condition one, and were looking for a second
condition for equilibrium (review condition 1)
B. What can we gain from this activity about the second condition for
equilibrium?
1. Our systems were balanced when there was no rotational motion.
2. There must be no net turning effect of forces rotating an object about a
pivot point.
3. When there was a net turning effect, what happened? (the object turned
or twisted) In what direction did the object turn or twist? (depends on which side had
more of a turning force)
III. Torque
A. What we have done here can be defined in a different way. The turning force
that made our objects turn when not in equilibrium is torque.
B. We can think of torque as a twist applied to an object to make that object turn
about its axis of rotation.
C. What two things in our activity mattered the most for the system to be
balanced? (distance of placement of paper clips, and number of paper clips)
D. These two items are how we find the magnitude of torque on an object.
1. T=F*D
2. It is a vector quantity (just like force)
3. The distance is defined as the distance between the applied force and
the axis of rotation (pivot point) and the force is defined as the perpendicular component
of the force.
4. The units for torque are N*m or lb*ft (as it is a force * a distance)
E. Use a weight hanging from the far end of a beam to demonstrate torque.
1. When torque is applied it changes an objects rate of rotational motion
2. The perpendicular component of force (the weight of the object) pulls
down on the beam more at the end than if the weight was at the middle.
F. Use door example to again reinforce the distance component. (harder to open
a door when pushing near the hinges, but when pushing at a distance from the hinges
(pivot point) it is easier to get a rotational motion) Have students try this
Unit 1: Balancing, Torque, and Stability
G. Use this diagram to help students understand this concept
IV. More examples of Torque
A. Using a wrench or changing a tire – when doing this you generate torque by
applying a force on the handle which creates a torque on the lug nut, which in turn creates
a rotational motion.
B Find another example
C. Car engine simulation (ADD WEBSITE)
V. Finding the torque (sample problems)
A. 1.
Find the torque exerted by the wrench on the bolt in the diagram below.
Unit 1: Balancing, Torque, and Stability
B. 2.
A student with an arm of length 2 ft holds a weight of 20 lb in her hand.
Calculate the torque exerted on her shoulder by the weight if she holds her arm a)
outstretched, b) at her side, and c) at an angle of 60˚ below horizontal.
a)
First draw a schematic diagram and then determine the torque using Eq. (7.1).
C. b)
We see that when the weight is held at her side there is no component of
the force perpendicular to d. This force gives no turning effect and thus the torque is
zero.
VI. Restate second equilibrium condition
A. Either draw a picture on board or put on overhead machine a picture of a
seesaw. How could be get an adult (150 lb) and a child (75lb) to balance on a seesaw?
1. Have students give the answer to this based on what they know already
2. Relate this back to the balancing acts activity
3. The child (half the weight) would have to sit twice as far from the pivot
point (or fulcrum) of the seesaw.
B. What would the net torque be of the system? ZERO
C. The second condition for equilibrium can be thought of as a situation where
there is a net torque of zero, not just a net force of zero as stated before. We can also
think of this as a situation in which the sum of all the clockwise (CW) torques must equal
the sum of all the counterclockwise (CCW) torques.
VII. Examples of equilibrium
Unit 1: Balancing, Torque, and Stability
A. 1.
A 16 ft seesaw is pivoted in the center. At what distance from the
center would a 200 lb person sit to balance a 150 lb person on the opposite end?
A convenient point to calculate the torques would be at the fulcrum. With this choice the
upward force exerted by the fulcrum does not contribute to the torques.
B. 2 Add in one more simple one from first torque sheet
C. 3.
A 10 ft, 25 lb seesaw is balanced by a little girl (50 lb) and her father
(200 lb) at opposite ends as shown below. How far from the seesaw’s center of mass
must the fulcrum be placed?
Calculate the torques about the fulcrum.
Unit 1: Balancing, Torque, and Stability
VIII. How can I get more torque?
A. Now that we know what torque is, how to calculate it, and how to find the
balance (equilibrium in a system, no net torque) we can look at how to increase torque.
B. What do you think are two ways of increasing torque? (write equation on
board for the class to look at)
1. Increase the force
2. Make your lever bigger (get a bigger wrench)
C. Also discuss the application of force and how it matters in the amount of
torque generated
1. Use this wrench diagram to explain which scenario allows for the
maximum torque.
IX. Summarize torque and provide any handouts