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:**
A DVD is rotating at 440 rpm. What is the angular momentum of the DVD if it has a radius of 6.00 cm and a mass of 22.0 g?
**Explanation:**
To solve this problem, we'll use the formula for angular momentum \( L \) of a rotating object:
\[ L = I \cdot \omega \]
where:
- \( I \) is the moment of inertia,
- \( \omega \) is the angular velocity in radians per second (rad/s).
**Calculating the Moment of Inertia \( I \):**
For a disc, the moment of inertia \( I \) is given by:
\[ I = \frac{1}{2} m r^2 \]
where:
- \( m = 22.0 \, \text{g} = 0.022 \, \text{kg} \) (converted to kilograms),
- \( r = 6.00 \, \text{cm} = 0.06 \, \text{m} \) (converted to meters).
**Converting \( I \):**
\[ I = \frac{1}{2} \times 0.022 \times (0.06)^2 \]
**Calculating Angular Velocity \( \omega \):**
To convert 440 rpm to rad/s:
\[ \omega = 440 \times \frac{2\pi}{60} \]
(Note: \( 2\pi \) radians is equal to one full rotation, and there are 60 seconds in a minute.)
**Final Calculation:**
Substitute the values for \( I \) and \( \omega \) into the formula for \( L \) to find the angular momentum.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02ec4b82-5ff0-4052-a25d-a8fd5708f2e2%2F30b359c5-bd92-4b7e-951d-5af237a4e810%2Fu0kqeyd_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A DVD is rotating at 440 rpm. What is the angular momentum of the DVD if it has a radius of 6.00 cm and a mass of 22.0 g?
**Explanation:**
To solve this problem, we'll use the formula for angular momentum \( L \) of a rotating object:
\[ L = I \cdot \omega \]
where:
- \( I \) is the moment of inertia,
- \( \omega \) is the angular velocity in radians per second (rad/s).
**Calculating the Moment of Inertia \( I \):**
For a disc, the moment of inertia \( I \) is given by:
\[ I = \frac{1}{2} m r^2 \]
where:
- \( m = 22.0 \, \text{g} = 0.022 \, \text{kg} \) (converted to kilograms),
- \( r = 6.00 \, \text{cm} = 0.06 \, \text{m} \) (converted to meters).
**Converting \( I \):**
\[ I = \frac{1}{2} \times 0.022 \times (0.06)^2 \]
**Calculating Angular Velocity \( \omega \):**
To convert 440 rpm to rad/s:
\[ \omega = 440 \times \frac{2\pi}{60} \]
(Note: \( 2\pi \) radians is equal to one full rotation, and there are 60 seconds in a minute.)
**Final Calculation:**
Substitute the values for \( I \) and \( \omega \) into the formula for \( L \) to find the angular momentum.
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