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An ice skater with her arms extended has a rotational inertia of 9.0 kg m² and spins at a rate of 1.0 revolution per second. (a) If she stays spinning in the same spot, what is her rotational kinetic energy? (b) What will her rate of rotation be when she pulls her arms in enough to reduce her rotational inertia to 2.5 kg m²? (c) Has her rotational kinetic energy changed in this process? If so, by how much?

An ice skater with her arms extended has a rotational inertia of 9.0 kg m² and spins at a rate of 1.0 revolution per second. (a) If she stays spinning in the same spot, what is her rotational kinetic energy? (b) What will her rate of rotation be when she pulls her arms in enough to reduce her rotational inertia to 2.5 kg m²? (c) Has her rotational kinetic energy changed in this process? If so, by how much?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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5. 1. 3. An ice skater with her arms extended has a rotational inertia of 9.0 kg m²2 and spins at a rate of 1.0 revolution per second. (a) If she stays spinning in the same spot, what is her rotational kinetic energy? (b) What will her rate of rotation be when she pulls her arms in enough to reduce her rotational inertia to 2.5 kg m²? (c) Has her rotational kinetic energy changed in this process? If so, by how much? 2. Two disks have the same axis of rotation. One is already spinning with frequency f in the horizontal plane when the second one is dropped onto it from above. If the disks have the same radius but the bottom one is 3 times as massive as the top one, the final frequency will be f. Why? (Be quantitative in your explanation.) astor doll [7.5 m If r= 2.7 m and p = 270 kg m/s , what is rx p? 0 4. A uniform, plastic meterstick of mass 48 g is set horizontally across the span between two tables so that its center is located exactly midway between the tables and its ends are barely on each table. (a) What is the magnitude of the force exerted by each table on the meterstick? (b) An 80 g mass is placed on the meterstick at the 80 cm mark. Now what is the magnitude of the force exerted by each table on the meterstick? The formula for a thin spherical shell's rotational inertia about an axis that goes through its center is mr². If a spherical shell rolls without slipping across a surface, it will have some total kinetic energy (both linear and rotational). Write an expression for this total kinetic energy in terms of just the mass m and the linear velocity v (assuming it rolls without slipping). Explain or show how you get your answer.
Transcribed Image Text:5. 1. 3. An ice skater with her arms extended has a rotational inertia of 9.0 kg m²2 and spins at a rate of 1.0 revolution per second. (a) If she stays spinning in the same spot, what is her rotational kinetic energy? (b) What will her rate of rotation be when she pulls her arms in enough to reduce her rotational inertia to 2.5 kg m²? (c) Has her rotational kinetic energy changed in this process? If so, by how much? 2. Two disks have the same axis of rotation. One is already spinning with frequency f in the horizontal plane when the second one is dropped onto it from above. If the disks have the same radius but the bottom one is 3 times as massive as the top one, the final frequency will be f. Why? (Be quantitative in your explanation.) astor doll [7.5 m If r= 2.7 m and p = 270 kg m/s , what is rx p? 0 4. A uniform, plastic meterstick of mass 48 g is set horizontally across the span between two tables so that its center is located exactly midway between the tables and its ends are barely on each table. (a) What is the magnitude of the force exerted by each table on the meterstick? (b) An 80 g mass is placed on the meterstick at the 80 cm mark. Now what is the magnitude of the force exerted by each table on the meterstick? The formula for a thin spherical shell's rotational inertia about an axis that goes through its center is mr². If a spherical shell rolls without slipping across a surface, it will have some total kinetic energy (both linear and rotational). Write an expression for this total kinetic energy in terms of just the mass m and the linear velocity v (assuming it rolls without slipping). Explain or show how you get your answer.
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