T 1. A uniform disk, such as a record turntable, initially turns at 5.00 rev/s around a frictionless spindle as shown below. A nonrotating uniform disk, half of the mass of the turntable disk and diameter equal to that of the turntable, is dropped from above onto the freely spinning turntable disk. They then both turn around the spindle with their centers superposed. a) Which concept can be used to solve for the angular velocity of the combination? Explain. b) Derive the algebraic expression for the angular velocity of the combination. c) Calculate the magnitude of the angular velocity of the combination.

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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### Physics Problem: Angular Velocity of Combined Disks

#### Problem Statement:
1. **Initial Conditions**: A uniform disk, such as a record turntable, initially turns at 5.00 revolutions per second (rev/s) around a frictionless spindle.
   
   **Scenario**: A non-rotating uniform disk, with half the mass of the turntable disk and a diameter equal to that of the turntable, is dropped from above onto the freely spinning turntable disk. They then both turn around the spindle with their centers superposed.

#### Questions and Tasks:
a) **Concept Identification**:
   - Which concept can be used to solve for the angular velocity of the combination? Explain.

b) **Algebraic Expression**:
   - Derive the algebraic expression for the angular velocity of the combination.

c) **Calculation**:
   - Calculate the magnitude of the angular velocity of the combination.

#### Diagram Description:
- The provided diagram illustrates two disks. 
  - The upper disk is non-rotating and about to be dropped onto the lower, rotating disk.
  - The arrow indicates the direction of rotation of the lower disk.

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This educational problem involves concepts of rotational motion and conservation of angular momentum. To solve it, you need a good understanding of how angular momentum works when multiple rotating objects interact.
Transcribed Image Text:--- ### Physics Problem: Angular Velocity of Combined Disks #### Problem Statement: 1. **Initial Conditions**: A uniform disk, such as a record turntable, initially turns at 5.00 revolutions per second (rev/s) around a frictionless spindle. **Scenario**: A non-rotating uniform disk, with half the mass of the turntable disk and a diameter equal to that of the turntable, is dropped from above onto the freely spinning turntable disk. They then both turn around the spindle with their centers superposed. #### Questions and Tasks: a) **Concept Identification**: - Which concept can be used to solve for the angular velocity of the combination? Explain. b) **Algebraic Expression**: - Derive the algebraic expression for the angular velocity of the combination. c) **Calculation**: - Calculate the magnitude of the angular velocity of the combination. #### Diagram Description: - The provided diagram illustrates two disks. - The upper disk is non-rotating and about to be dropped onto the lower, rotating disk. - The arrow indicates the direction of rotation of the lower disk. --- This educational problem involves concepts of rotational motion and conservation of angular momentum. To solve it, you need a good understanding of how angular momentum works when multiple rotating objects interact.
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