GIZMOS > Western Connecticut State University PHY 170  Moment of Inertia Turntable Gizmo Answers.

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Student Exploration: Moment of Inertia Vocabulary: angular velocity, linear velocity, moment of inertia, rotational KE, translational KE 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 angular velocity increases 2. Why do you think this will happen? her arms have a greater momentum outstretched than when they are pulled closer to her body 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? spins the same speed 2. The speed of rotation is described by angular velocity (ω), which is measured in radians per second. There are 2π radians (6.28 radians) in a circle. What is the current angular velocity? 4.00 rad/s 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? 20.0 rads/s B. How is this situation similar to a spinning skater? the ball is moving faster as the center of gravity is closer C. How does this relate to position of mass on a see-saw? Activity A: Angular velocity Get the Gizmo ready: ● Click Reset. ● 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 2π 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? the more mass that you add to the angular velocity the more mass you add to less angular velocity there is B. How does increasing the average distance of the masses from the center affect the angular velocity of the turntable? as you increase the distance there is even loss angular velocity 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: 20 10 6.67 5 4 3.33 Linear velocity: 1000 50 33.33 25 200 16.67 3. Analyze: How does the linear velocity relate to the angular velocity and the radius? the linear velocity relates to the angular velocity and the radius Write an equation for the linear velocity (v) based on angular velocity (ω) and position of the red dot (r): [Show More]

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