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A 80kg student is running with a speed of 4.5m/s when she leaps onto a disc- shaped play ground toy at the position shown. The 110kg disc is free to around it's fixed center and has a radius of 1.3m. The moment of inertia of a point (like the student) is I = mr2. The moment of inertia top view: of any disc is I = 1/2mr?. 0.8m Determine all of the following moments of inertia, angular speeds and angular momenta relative to the center of the disc. side view: kg m2 v rad/s v kg m2/s v student (running) disc (rest) combined How quickly will the disc and student spin (in given units)? rpm

A 80kg student is running with a speed of 4.5m/s when she leaps onto a disc- shaped play ground toy at the position shown. The 110kg disc is free to around it's fixed center and has a radius of 1.3m. The moment of inertia of a point (like the student) is I = mr2. The moment of inertia top view: of any disc is I = 1/2mr?. 0.8m Determine all of the following moments of inertia, angular speeds and angular momenta relative to the center of the disc. side view: kg m2 v rad/s v kg m2/s v student (running) disc (rest) combined How quickly will the disc and student spin (in given units)? rpm

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
Section: Chapter Questions
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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**Title: Understanding Angular Momentum in Rotational Mechanics** **Problem Setup:** An 80 kg student is running at a speed of 4.5 m/s when she leaps onto a disc-shaped playground toy positioned as shown in the diagram. The disc, which weighs 110 kg, is free to rotate around its fixed center and has a radius of 1.3 meters. **Important Concepts and Equations:** - **Moment of Inertia:** - For a point like the student, \( I = mr^2 \). - For a disc, \( I = \frac{1}{2}mr^2 \). - **Angular Speed (\(\omega\)):** - Angular speed is measured in radians per second (rad/s). - **Angular Momentum (\(L\)):** - Calculated as \( L = I \cdot \omega \). **Task:** Determine the following relative to the center of the disc: 1. Moment of inertia for the student, disc, and combined system. 2. Angular speeds for the student, disc, and combined system. 3. Angular momenta for the student, disc, and combined system. **Diagrams:** 1. **Top View:** - The disc is shown with a radius marked as 0.8 meters, with the student jumping onto it. 2. **Side View:** - Illustrates the student running and then leaping onto the disc. **Data Table to Complete:** | | \( I \) (kg m²) | \( \omega \) (rad/s) | \( L \) (kg m²/s) | |-----------------------|-----------------|----------------------|--------------------| | student (running) | | | | | disc (at rest) | | | | | combined system | | | | **Final Question:** How quickly will the disc and student spin together (in given units of rpm)? **Explanation of Concepts Illustrated in Diagrams:** - **Top View:** - Shows the rotation radius from the center of the disc to the point where the student makes contact. - **Side View:** - Depicts the sequence of motion of the student as she leaps onto the disc, transitioning from linear to rotational movement. To solve the problem, follow these steps: 1. Calculate the individual moments of inertia:
Transcribed Image Text:**Title: Understanding Angular Momentum in Rotational Mechanics** **Problem Setup:** An 80 kg student is running at a speed of 4.5 m/s when she leaps onto a disc-shaped playground toy positioned as shown in the diagram. The disc, which weighs 110 kg, is free to rotate around its fixed center and has a radius of 1.3 meters. **Important Concepts and Equations:** - **Moment of Inertia:** - For a point like the student, \( I = mr^2 \). - For a disc, \( I = \frac{1}{2}mr^2 \). - **Angular Speed (\(\omega\)):** - Angular speed is measured in radians per second (rad/s). - **Angular Momentum (\(L\)):** - Calculated as \( L = I \cdot \omega \). **Task:** Determine the following relative to the center of the disc: 1. Moment of inertia for the student, disc, and combined system. 2. Angular speeds for the student, disc, and combined system. 3. Angular momenta for the student, disc, and combined system. **Diagrams:** 1. **Top View:** - The disc is shown with a radius marked as 0.8 meters, with the student jumping onto it. 2. **Side View:** - Illustrates the student running and then leaping onto the disc. **Data Table to Complete:** | | \( I \) (kg m²) | \( \omega \) (rad/s) | \( L \) (kg m²/s) | |-----------------------|-----------------|----------------------|--------------------| | student (running) | | | | | disc (at rest) | | | | | combined system | | | | **Final Question:** How quickly will the disc and student spin together (in given units of rpm)? **Explanation of Concepts Illustrated in Diagrams:** - **Top View:** - Shows the rotation radius from the center of the disc to the point where the student makes contact. - **Side View:** - Depicts the sequence of motion of the student as she leaps onto the disc, transitioning from linear to rotational movement. To solve the problem, follow these steps: 1. Calculate the individual moments of inertia:
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