Gizmo Labs-Moment of Inertia Student Exploration (pdf) - Course Sidekick (2024)

8/10/23, 3:28 PMGizmo Labs-Moment of Inertia Student Exploration about:blank1/6Name:Date: 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? The skater will spin faster as she pulls her arms in and stands up straight. 2.Why do you think this will happen? This is because the center of her mass is in the middle. Gizmo Warm-up TheMoment of InertiaGizmo 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.ClickPlay(). What happens? The turntable spins. 2.The speed of rotation is described by), which is measured in radians per second. angular velocity(ωThere are 2radians (6.28 radians) in a circle. πWhat is the current angularvelocity? ω= 4 radians per second 3.ClickReset(). Move the mass so that it is only 1 meter from the center (= 1). rA.ClickPlay. What is the angular velocity now?ω= 20 radians per second B.How is this situation similar to a spinning skater?It spins faster the closer the mass is to the center. Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved

8/10/23, 3:28 PMGizmo Labs-Moment of Inertia Student Exploration about:blank2/6Activity A: Angular velocity Get the Gizmo ready: ●Click. Reset●Check that theis set to 200 J. Piston energyIntroduction: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) of a point on the turntable. Linear velocity is simply the speed and linear velocity(vdirection 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? Increasing the mass would require more energy to move it. So the turntable would 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 will remain the same. 2.Gather data: Turn on. The Gizmo reports the velocity of the red dot. Show linear velocityPlace the red dot at 1 meter and a single mass at 5 meters. Click. For each position of the red dot, Playrecord the angular velocity of the turntable and linear velocity of the red dot. Red dot position:r= 1 mr= 2 mr= 3 mr= 4 mr= 5 mr= 6 m Angular velocity:4 rad/s4 rad/s4 rad/s4 rad/s4 rad/s4 rad/s Linear velocity:4 m/s8 m/s12 m/s16 m/s20 m/s24 m/s 3.Analyze: How does the linear velocity relate to the angular velocity and the radius? The linear velocity is the product of the angular velocity and the radius Write an equation for the linear velocity () based on angular velocity () and position of the red dot (vωr): v=ωr Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved

8/10/23, 3:28 PMGizmo Labs-Moment of Inertia Student Exploration about:blank3/64.Gather data: Place a single mass on the turntable at a radius of 6 m, and place the red dot on the mass. ClickPlay, and record both the angular velocity () of the turntable and the linear velocity () of the mass. ωvMove the massred dot to the next radius and repeat. andRadius (m)Angular velocity (rad/s)Linear velocity (m/s)Kinetic energy (J) 6 m3.33 rad/s20 m/s200 J 3 m6.67 rad/s20 m/s200 J 2 m10 rad/s20 m/s200 J 5.Analyze: What patterns do you notice in your data? The angular velocity is the only one that does not remain the same when the radius changes. 6.Calculate: Theof a rotating object is equal to one half its mass multiplied by translational kinetic energyits velocity squared:= ½. Use the linear velocity to calculate the last column of the table. (Hint: TKEmv2There is one mass on the turntable, so its mass is 1 kg.) A.How does the translational kinetic energy of the turntable compare to the piston energy? 0.5 (1) (20)^2=200 J B.Why do you think this is so? Because of the conservation of energy, the piston energy must equal the acceleration energy. 7.Manipulate: Suppose a weightless turntable contains a single massthat is a distancefrom the center. mrThe turntable has a kinetic energy. KEA.How would you calculate the linear velocity of the mass?v=sqrt (2KE/m) B.How would you calculate the angular velocity of theturntable? ω=v/r C.Given the radius r, the mass m, and the kinetic energy KE,what is the angular velocity of the turntable? ω=(sqrt (2KE/m))/r 8.Apply: A weightless turntable has a mass of 4 kg thatis located 3 m from the center. It is struck by a piston that imparts 160 J of kinetic energy to the turntable. What is the angular velocity of theturntable? 2.98 rad/s Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved

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