Torque Moment Inertia SE – Name: Adam Date: Student Exploration: Torque and Moment of Inertia – Studocu
Name: Adam Date:
Student Exploration: Torque and Moment of Inertia
Directions: Follow the instructions to go through the simulation. Respond to the questions and
prompts in the orange boxes.
Vocabulary: angular acceleration, fulcrum, lever, moment of inertia, Newton’s second law, torque, weight
Prior Knowledge Question (Do this BEFORE using the Gizmo.)
During recess, Tom and his little sister Marcie want to play on the see-saw. Tom is quite a bit heavier than
Marcie. Where should they sit so the see-saw is balanced? Sketch their positions on the image below.
Explain your reasoning:
Tom should sit closer to the center of
the seesaw than Marcie. She should be
closer to the end on her side. This is
because the triangle in the center will
help balance out the weight difference if
Tom sits closer to it.
Gizmo Warm-up
The Torque and Moment of Inertia Gizmo shows a see-saw,
which is a type of lever. The see-saw can hold up to eight
objects. To begin, check that the Number of objects is 2. Check
that the mass of object A is 1 kg and the mass of object B is
2 kg. The two objects are equidistant from the triangular
fulcrum that supports the lever.
- Click Release. What happens?
The lever falls to the right
- Click Reset. Without changing the masses, experiment with different positions of objects A and B by
dragging them around.
Can you create a scenario in which object A goes down and object B goes up? yes
Explain: Object A has to be placed far away from the fulcrum and object B close to it.
- Can you create a scenario in which object A perfectly balances object B? yes
Explain: Object A has to move a little ways away from the fulcrum to balance out object
B.
✏️ Either hand draw or click here
to EDIT to use the drawing tool.
Activity A:
Principle of the
lever
Get the Gizmo ready:
●Click Reset. Turn on Show ruler.
●Check that object A is 1 kg and B is 2 kg.
Question: How can you use a light object to balance a heavy object?
- Explore : Experiment with the Gizmo to see how you can balance a heavy object with a light object. What
do you notice about the distances of each object from the fulcrum?
The lighter object is further away from the fulcrum than the heavier object.
- Gather data : For each mass and location of object A , find a location for object B so it perfectly balances
object A. You can change the mass of object A by typing the mass into the text box and hitting “Enter” on
your keyboard. Leave the mass of object B the same
(1 kg) in each experiment. Include all units in the table.
Object A
mass
Object A
location
Object B
mass
Object B
location
Object A
m × d
Object B
m × d
1 kg -0 m 1 kg 0 m 0 kgm 0 kgm
2 kg -0 m 1 kg 0 m 0 kgm 0 kgm
3 kg -0 m 1 kg 1 m 1 kgm 1 kgm
4 kg -0 m 1 kg 1 m 1 kgm 1 kgm
- Analyze : What patterns do you notice in your data?
When Object A’s mass increased, object B had to move further from the fulcrum.
- Calculate : Fill in the last two columns by multiplying each object’s mass by its distance from the fulcrum.
The units are kg·m. (Note: The distance d is always a positive number.)
What do you notice? They are equal.
- Generalize : In general, how can you calculate the distance of object B from the fulcrum so that it balances
object A?
Multiply object A’s mass and distance and then divide that by the mass of Object B.
- Apply : Suppose you wanted to lift a heavy rock with a lever. Would you place the fulcrum near the rock or
near the part of the lever where you are pushing? Explain.
I would place it near the rock so that the lever can push the rock upwards with less mass on the other
end of it.
- Apply : What is the torque exerted by a 4-kg mass that is located 1 m to the right of the fulcrum?
-74 Nm Check your answer with the Gizmo.
- Explore : Set the Number of objects to 2. Set the Mass of object A to 5 kg and its Location to 1 m. Set
the Mass of object B to 3 kg and is Location to 0 m.
A. What torque does object A exert on the see-saw? 58 Nm
B. What torque does object B exert on the see-saw? 14 Nm
C. What do you think is the total torque on the see-saw? -73 Nm
D. Check that Show initial torque is on and click Release.
What is the total torque? -73 Nm
- Practice : A lever supports four objects:
● Object A is 3 kg and located 2 m left
of the fulcrum.
● Object B is 7 kg and located 0 m left
of the fulcrum.
● Object C is 8 kg and located 0 m
right of the fulcrum.
● Object D is 4 kg and located 1 m
right of the fulcrum.
A. What is the total torque on the lever? 14 Nm
(Hint: Recall that objects to the right of the fulcrum will have a negative torque.)
Show your work: a- 58 b-34 Nm c- -7 d- -70
B. When released, will the left rotate clockwise or counterclockwise? counterclockwise
C. Check your answers on the Gizmo. Were you correct? off by 0 Nm
- Explain : If two kids are playing on the see-saw, why should the larger kid sit closer to the fulcrum than the
smaller kid? Use the term “torque” in your explanation.
The larger kid should sit closer to the fulcrum than the smaller kid so that the position can raise the
torque that the smaller kid exerts on the lever to balance them out.
Activity C:
Moment of inertia
Get the Gizmo ready:
●Click Reset.
●Check that the Number of objects is 1.
●Set Mass A to 2 kg.
Introduction: When describing the motion of rotating objects (such as see-saws), physicists use several terms
that are equivalent to those used for linear motion. For example, torque ( τ ) is the rotational equivalent of force,
while angular acceleration ( α ) is the rotational equivalent of linear acceleration.
Question: What factors affect how quickly a see-saw accelerates?
- Predict : Two children of equal mass decide to have a see-saw race. Each child sits on an identical see-saw
with nothing on the other side. Mikhi sits at the end of his see-saw as far away as possible from the
fulcrum. Katelyn sits near the middle of her see-saw close to the fulcrum. Their friends lift both see-saws to
the top and release them simultaneously.
Which see-saw do you think will hit the ground first, and why?
I think Katelyn will hit the ground first because since she is sitting closer to the fulcrum, she has less
distance to travel to the ground.
- Experiment : Move object A to the end of the see-saw as far as possible from the fulcrum. Click Release ,
and record how long it takes for the see-saw to hit the ground. Click Reset and place object A close to the
fulcrum. Click Release and record the time again.
Time to hit ground when object A is far from the fulcrum: 0 sec
Time to hit ground when object A is close to the fulcrum: 0 sec
- Compare : The rate at which a rotating object accelerates is related to its moment of inertia. Click Reset.
Turn on Show moment of inertia and compare the moment of inertia for a mass close to the fulcrum and
the same mass far from the fulcrum. (Click Release to see the moment of inertia.) How does moment of
inertia relate to the distance to the fulcrum?
The closer to the fulcrum an object sits, the lower the moment of inertia is.
- Calculate : Place a 5-kg mass 2 m from the fulcrum. To find the moment of inertia for a mass located a
distance r from the fulcrum, use the equation: I = mr 2.
What is the moment of inertia of this mass? 20 kg·m 2 (Note: Units are kg·m 2 .)
Check your answer by turning on Show moment of inertia and clicking Release.
- Compare : You may have been surprised that the see-saw accelerated more slowly when the mass was far
from the fulcrum and the torque was greater. That is because the angular acceleration of the see-saw
depends on two factors: torque and moment of inertia ( I ). Just as mass is a measure of an object’s
resistance to acceleration, moment of inertia is a measure of an object’s resistance to angular acceleration.
