(a) the angular velocity in rad/s and (b) the period of the motion? Express your answer with the appropriate units. ON Value Submit Part B μА O Submit Value undo Express your answer with the appropriate units. μA Units Request Answer Units ? Request Answer ?
(a) the angular velocity in rad/s and (b) the period of the motion? Express your answer with the appropriate units. ON Value Submit Part B μА O Submit Value undo Express your answer with the appropriate units. μA Units Request Answer Units ? Request Answer ?
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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Angular speed, acceleration and displacement
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Angular Position
Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.
Question
![**Question:**
An old-fashioned single-play vinyl record rotates on a turntable at 45.0 rpm. What are (a) the angular velocity in rad/s and (b) the period of the motion?
**Solution:**
To solve this problem, we need to convert the given rotational speed from revolutions per minute (rpm) to the desired units: radians per second (rad/s) for angular velocity and seconds for period.
**Part A: Angular Velocity**
- Angular velocity (ω) in rad/s can be found using the conversion:
- \( 1 \text{ revolution} = 2\pi \text{ radians} \)
- \( 1 \text{ minute} = 60 \text{ seconds} \)
- Given \( \text{speed} = 45 \text{ rpm} \), the conversion is:
\[
\omega = 45 \times \frac{2\pi \text{ rad}}{1 \text{ rev}} \times \frac{1 \text{ min}}{60 \text{ s}}
\]
**Answer Placeholder:**
Express your answer with the appropriate units:
\[ \underline{\hspace{100pt}} \text{ rad/s} \]
**Part B: Period of Motion**
- The period (T) is the time taken for one complete revolution, which is the reciprocal of the frequency.
- Frequency in revolutions per second (rps) is:
\[
f = \frac{45 \text{ rev/min}}{60 \text{ s/min}} = \frac{45}{60} \text{ rps}
\]
- Period (\(T\)) is the reciprocal of frequency:
\[
T = \frac{1}{f} = \frac{60}{45} \text{ s}
\]
**Answer Placeholder:**
Express your answer with the appropriate units:
\[ \underline{\hspace{100pt}} \text{ s} \]
**Interactive Part:**
For both parts, students can input their answers in the provided boxes and submit to check their understanding of the concepts.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb365fa56-db01-4f82-bc2c-5bb5151e447e%2Facd75808-58b7-49ad-a398-5481b8b0270d%2Fjz88499_processed.png&w=3840&q=75)
Transcribed Image Text:**Question:**
An old-fashioned single-play vinyl record rotates on a turntable at 45.0 rpm. What are (a) the angular velocity in rad/s and (b) the period of the motion?
**Solution:**
To solve this problem, we need to convert the given rotational speed from revolutions per minute (rpm) to the desired units: radians per second (rad/s) for angular velocity and seconds for period.
**Part A: Angular Velocity**
- Angular velocity (ω) in rad/s can be found using the conversion:
- \( 1 \text{ revolution} = 2\pi \text{ radians} \)
- \( 1 \text{ minute} = 60 \text{ seconds} \)
- Given \( \text{speed} = 45 \text{ rpm} \), the conversion is:
\[
\omega = 45 \times \frac{2\pi \text{ rad}}{1 \text{ rev}} \times \frac{1 \text{ min}}{60 \text{ s}}
\]
**Answer Placeholder:**
Express your answer with the appropriate units:
\[ \underline{\hspace{100pt}} \text{ rad/s} \]
**Part B: Period of Motion**
- The period (T) is the time taken for one complete revolution, which is the reciprocal of the frequency.
- Frequency in revolutions per second (rps) is:
\[
f = \frac{45 \text{ rev/min}}{60 \text{ s/min}} = \frac{45}{60} \text{ rps}
\]
- Period (\(T\)) is the reciprocal of frequency:
\[
T = \frac{1}{f} = \frac{60}{45} \text{ s}
\]
**Answer Placeholder:**
Express your answer with the appropriate units:
\[ \underline{\hspace{100pt}} \text{ s} \]
**Interactive Part:**
For both parts, students can input their answers in the provided boxes and submit to check their understanding of the concepts.
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