Two spheres are each rotating at an angular speed of 25.0 rad/s about axes that pass through their centers. Each has a radius of 0.460m and a mass of 1.66 kg. However, as the figure shows, one is solid and the other is a thin-walled spherical shell. Suddenly, a net external torque due to friction (magnitude = 0.360 N · m) begins to act on each sphere and slows the motion down. How long does it take (a) the solid sphere and (b) the thin-walled sphere to come to a halt?
Two spheres are each rotating at an angular speed of 25.0 rad/s about axes that pass through their centers. Each has a radius of 0.460m and a mass of 1.66 kg. However, as the figure shows, one is solid and the other is a thin-walled spherical shell. Suddenly, a net external torque due to friction (magnitude = 0.360 N · m) begins to act on each sphere and slows the motion down. How long does it take (a) the solid sphere and (b) the thin-walled sphere to come to a halt?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Two spheres are each rotating at an angular speed of 25.0 rad/s about axes that pass through their centers. Each has a radius of 0.460m and a mass of 1.66 kg. However, as the figure shows, one is solid and the other is a thin-walled spherical shell. Suddenly, a net external torque due to friction (magnitude = 0.360 N · m) begins to act on each sphere and slows the motion down. How long does it take (a) the solid sphere and (b) the thin-walled sphere to come to a halt?
Transcribed Image Text:The image presents two types of spheres, both depicted with rotational motion indicated by an arrow labeled ω (omega), which represents angular velocity.
1. **Solid Sphere**:
- The illustration shows a solid sphere rotating about an axis. The entire volume of the sphere contributes to its rotational inertia. This type of sphere has mass distributed throughout its volume.
2. **Thin-Walled Spherical Shell**:
- This image shows a thin-walled spherical shell also rotating about an axis. Unlike the solid sphere, the mass is concentrated along the thin outer shell, with the interior being hollow. A small cutout is depicted to highlight the shell nature.
These diagrams help in understanding different moments of inertia depending on how mass is distributed in objects with similar shapes but varying internal structures.
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