What is the angular momentum L, of a 0.300-kg tetherball when it whirls around the central pole at 40.0 rpm and at a radius of 115 cm?

College Physics
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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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### 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.
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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