33) At a certain instant, a compact disc is rotating at 210 rpm. What is its angular speed in rad/s? Show work. A) 11 rad/s B) 22frad/s C) 45 rad/s D) 69 rad/s E) 660 rad/s 34) A child is riding a merry-go-round that is turning at 7.18 rpm. If the child is standing 4.65 m from the center of the merry-go-round, how fast is the child moving? Show work. A) 5.64 m/s B) 3.50 m/s C) 0.556 m/s D) 1.75 m/s E) 1.80 m/s
33) At a certain instant, a compact disc is rotating at 210 rpm. What is its angular speed in rad/s? Show work. A) 11 rad/s B) 22frad/s C) 45 rad/s D) 69 rad/s E) 660 rad/s 34) A child is riding a merry-go-round that is turning at 7.18 rpm. If the child is standing 4.65 m from the center of the merry-go-round, how fast is the child moving? Show work. A) 5.64 m/s B) 3.50 m/s C) 0.556 m/s D) 1.75 m/s E) 1.80 m/s
College Physics
10th Edition
ISBN:9781285737027
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter8: Rotational Equilibrium And Rotational Dynamics
Section: Chapter Questions
Problem 3WUE
Related questions
Question
Please answer 33-34
![### Angular Speed and Linear Speed Problems
#### Problem 33
**Question:**
At a certain instant, a compact disc is rotating at 210 rpm. What is its angular speed in rad/s? **Show work.**
**Options:**
A) 11 rad/s
B) 22π rad/s
C) 45 rad/s
D) 69 rad/s
E) 660 rad/s
**Explanation:**
To find the angular speed in radians per second (rad/s) from the given revolutions per minute (rpm), use the conversion factor:
\[ 1 \, \text{rpm} = \frac{2π \, \text{rad}}{60 \, \text{s}} \]
#### Problem 34
**Question:**
A child is riding a merry-go-round that is turning at 7.18 rpm. If the child is standing 4.65 m from the center of the merry-go-round, how fast is the child moving? **Show work.**
**Options:**
A) 5.64 m/s
B) 3.50 m/s
C) 0.556 m/s
D) 1.75 m/s
E) 1.80 m/s
**Explanation:**
To find the linear speed (v) of the child, we first need to find the angular speed (ω) in rad/s:
\[ ω = 7.18 \, \text{rpm} \times \frac{2π \, \text{rad}}{60 \, \text{s}} = 0.75 \, \text{rad/s} \]
Then use the formula for linear speed:
\[ v = ω \times r \]
where \( r \) is the radius (4.65 m).
**Solution:**
\[ ω = 7.18 \times \frac{2π}{60} \approx 0.75 \, \text{rad/s} \]
\[ v = 0.75 \times 4.65 \approx 3.49 \, \text{m/s} \]
Thus the closest answer is:
B) 3.50 m/s
### Additional Information
Ensure to show each step of your work clearly and indicate the correct units for each calculation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbc6b83f6-6fd0-4bf2-b4c8-4ee11df5765c%2Fc6cdad15-285b-45d2-8cd5-8248e6084d5d%2Fmvvs3yp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Angular Speed and Linear Speed Problems
#### Problem 33
**Question:**
At a certain instant, a compact disc is rotating at 210 rpm. What is its angular speed in rad/s? **Show work.**
**Options:**
A) 11 rad/s
B) 22π rad/s
C) 45 rad/s
D) 69 rad/s
E) 660 rad/s
**Explanation:**
To find the angular speed in radians per second (rad/s) from the given revolutions per minute (rpm), use the conversion factor:
\[ 1 \, \text{rpm} = \frac{2π \, \text{rad}}{60 \, \text{s}} \]
#### Problem 34
**Question:**
A child is riding a merry-go-round that is turning at 7.18 rpm. If the child is standing 4.65 m from the center of the merry-go-round, how fast is the child moving? **Show work.**
**Options:**
A) 5.64 m/s
B) 3.50 m/s
C) 0.556 m/s
D) 1.75 m/s
E) 1.80 m/s
**Explanation:**
To find the linear speed (v) of the child, we first need to find the angular speed (ω) in rad/s:
\[ ω = 7.18 \, \text{rpm} \times \frac{2π \, \text{rad}}{60 \, \text{s}} = 0.75 \, \text{rad/s} \]
Then use the formula for linear speed:
\[ v = ω \times r \]
where \( r \) is the radius (4.65 m).
**Solution:**
\[ ω = 7.18 \times \frac{2π}{60} \approx 0.75 \, \text{rad/s} \]
\[ v = 0.75 \times 4.65 \approx 3.49 \, \text{m/s} \]
Thus the closest answer is:
B) 3.50 m/s
### Additional Information
Ensure to show each step of your work clearly and indicate the correct units for each calculation.
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