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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Question
![### Problem Statement
**Objective:** Calculate the angular momentum \( L_z \) of a tetherball.
**Parameters Provided:**
- Mass of the tetherball: 0.300 kg
- Rotation speed: 40.0 rpm (revolutions per minute)
- Radius of rotation: 115 cm
**Formula to Use:**
To find the angular momentum \( L_z \), you can use the formula:
\[ L_z = I \cdot \omega \]
Where:
- \( I \) is the moment of inertia
- \( \omega \) is the angular velocity in radians per second
**Steps to Solve:**
1. **Convert the radius to meters:** 115 cm = 1.15 m
2. **Convert the rpm to rad/s:**
\[
\omega = 40.0 \, \text{rpm} \times \frac{2\pi \, \text{rad}}{1 \, \text{rev}} \times \frac{1 \, \text{min}}{60 \, \text{s}}
\]
3. **Calculate the moment of inertia \( I \) for a point mass:**
\[ I = m \cdot r^2 \]
where \( m = 0.300 \, \text{kg} \) and \( r = 1.15 \, \text{m} \)
4. **Calculate \( L_z = I \cdot \omega \)**
**Answer Box:**
\[ L_z = \boxed{\phantom{} \, \text{kg} \cdot \text{m}^2/\text{s}} \]
Fill in the calculated value of \( L_z \) in the answer box.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe496cfb4-14de-4877-8074-43f9c7c49581%2Fb45784a3-a4c4-4781-973a-3ab4a86ec717%2Fqrkndz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
**Objective:** Calculate the angular momentum \( L_z \) of a tetherball.
**Parameters Provided:**
- Mass of the tetherball: 0.300 kg
- Rotation speed: 40.0 rpm (revolutions per minute)
- Radius of rotation: 115 cm
**Formula to Use:**
To find the angular momentum \( L_z \), you can use the formula:
\[ L_z = I \cdot \omega \]
Where:
- \( I \) is the moment of inertia
- \( \omega \) is the angular velocity in radians per second
**Steps to Solve:**
1. **Convert the radius to meters:** 115 cm = 1.15 m
2. **Convert the rpm to rad/s:**
\[
\omega = 40.0 \, \text{rpm} \times \frac{2\pi \, \text{rad}}{1 \, \text{rev}} \times \frac{1 \, \text{min}}{60 \, \text{s}}
\]
3. **Calculate the moment of inertia \( I \) for a point mass:**
\[ I = m \cdot r^2 \]
where \( m = 0.300 \, \text{kg} \) and \( r = 1.15 \, \text{m} \)
4. **Calculate \( L_z = I \cdot \omega \)**
**Answer Box:**
\[ L_z = \boxed{\phantom{} \, \text{kg} \cdot \text{m}^2/\text{s}} \]
Fill in the calculated value of \( L_z \) in the answer box.
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