Moment of Inertia Gizmo-ALL ANSWERS CORRECT-VERIFIED 2021

Name: Abril Guillen Moreno Date: 1/19/2021

Directions: Follow the instructions to go through the simulation. Respond to the questions and
prompts in the orange boxes.

Student Exploration: Moment of Inertia
Vocabulary​:​ angular velocity, linear velocity, moment of inertia, rotational kinetic energy, translational kinetic
energy

Prior Knowledge Questions ​(Do these BEFORE using the Gizmo.)
At the finale of her routine, a figure skater starts to spin slowly in the middle of the ice rink,
her arms and legs artfully outstretched.

1. What will happen as she stands up straight and pulls her arms in?

Her speed would increase.

2. Why do you think this will happen?

This is due to the fact that the center of mass is centrally located in the
middle.

Gizmo Warm-up
The ​Moment of Inertia​ Gizmo allows you to explore
the factors that affect how quickly objects spin. The
Gizmo shows a weightless turntable with several
pegs. You can place the purple 1-kg masses on
any of the pegs. When the Gizmo opens, there is a
single 1-kg mass located 5 m from the center.

1. Click ​Play ​( ). What happens?

The table spins.

2. The speed of rotation is described by ​angular velocity​ (​ω​), which is measured in radians per second.
There are 2​π​ radians (6.28 radians) in a circle.

What is the current angular ​ 4 rad/s
ω=
velocity?

3. Click ​Reset ​( ). Move the mass so that it is only 1 meter from the center (​r​ = 1).

A. Click ​Play​. What is the angular velocity now? ​ 20 rad/s
ω=


B. How is this situation similar to a spinning skater? The closer the mass gets to
the center the more its


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, speed increases.




Activity A: Get the Gizmo ready​:
● Click ​Reset​.
Angular velocity ● Check that the ​Piston energy​ is set to 200 J.

Introduction:​ For a spinning turntable, two types of velocity are important. As you learned, the angular velocity
(​ω​) describes how quickly the whole disk is spinning in radians per second. An angular velocity of 6.28 rad/s
describes a disk that makes one full revolution every second.

You can also describe the ​linear velocity​ (​v)​ of a point on the turntable. Linear velocity is simply the speed
and direction of a point at an instant in time. Linear velocity is measured in meters per second.

Question: How can you predict angular velocity based on the total energy of the turntable and how its
mass is distributed?

1. Explore​: Experiment with the Gizmo to answer the following two questions:

A. How does increasing the mass of the turntable affect its angular velocity?


It takes more energy from the piston to move it, and therefore it will move slower.


B. How does increasing the average distance of the masses from the center affect the angular velocity
of the turntable?


The angular velocity would be the same.


2. Gather data​: Turn on ​Show linear velocity​. The Gizmo reports the velocity of the red dot.

Place the red dot at 1 meter and a single mass at 5 meters. Click ​Play​. For each position of the red dot,
record the angular velocity of the turntable and linear velocity of the red dot.

Red dot position: r​ = 1 m r​ = 2 m r​ = 3 m r​ = 4 m r​ = 5 m r​ = 6 m
Angular velocity: 4 rad/s 4 rad/s 4 rad/s 4 rad/s 4 rad/s 4 rad/s
Linear velocity: 4 m/s 8 m/s 12 m/s 16 m/s 20 m/s 24 m/s

3. Analyze​: How does the linear velocity relate to the angular velocity and the radius?


The linear velocity is the radius times the angular velocity.


Write an equation for the linear velocity (​v)​ based on angular velocity (​ω)​ and position of the red dot (​r​):


v= ωr​



Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved