Take the radius of the Earth to be 6,378 km. (a) What is the angular speed (in rad/s) of a point on Earth's surface at latitude 31° N? 0.0000727 rad/s (b) What is the linear speed (in m/s) of a point on Earth's surface at latitude 31° N? 397.45 m/s (c) At what latitude would your linear speed be 32 m/s? (Enter your answer in degrees north of the equator.) 76.52 |× °N
Take the radius of the Earth to be 6,378 km. (a) What is the angular speed (in rad/s) of a point on Earth's surface at latitude 31° N? 0.0000727 rad/s (b) What is the linear speed (in m/s) of a point on Earth's surface at latitude 31° N? 397.45 m/s (c) At what latitude would your linear speed be 32 m/s? (Enter your answer in degrees north of the equator.) 76.52 |× °N
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Chapter1: Units, Trigonometry. And Vectors
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![# Earth Rotational Speed Calculation
Take the radius of the Earth to be 6,378 km.
### (a) Angular Speed Calculation
**Problem:** What is the angular speed (in rad/s) of a point on Earth's surface at latitude 31° N?
**Answer:**
\[ \text{Angular Speed} = 0.0000727 \, \text{rad/s} \]
A green check mark indicates the answer is correct.
### (b) Linear Speed Calculation
**Problem:** What is the linear speed (in m/s) of a point on Earth's surface at latitude 31° N?
**Answer:**
\[ \text{Linear Speed} = 397.45 \, \text{m/s} \]
A green check mark indicates the answer is correct.
### (c) Latitude Calculation for a Given Linear Speed
**Problem:** At what latitude would your linear speed be 32 m/s? (Enter your answer in degrees north of the equator.)
**Answer:**
\[ \text{Latitude} = 76.52° \, \text{N} \]
A red cross indicates the answer is incorrect.
### Explanation of Diagrams
There are no visual diagrams or graphs provided in the text. The calculations are presented in tabular form with individual problem statements and their corresponding answers.
For further understanding, these calculations relate to the Earth's rotation. The angular speed refers to how fast an object moves through an angle (in radians) over time. The linear speed relates to the actual distance an object moves along Earth's surface over time.
**Note:** The incorrect result for the latitude in part (c) suggests a need to either reperform the calculations or analyze the method for any potential errors.
---
This exercise demonstrates important concepts in Earth's rotational dynamics, which can have applications in various scientific fields, such as geography, astronomy, and physics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd0afef86-41bd-49f7-9deb-bb70dd2f5172%2F2f371501-6107-4a6d-8aeb-28b895f399de%2Floxatn.png&w=3840&q=75)
Transcribed Image Text:# Earth Rotational Speed Calculation
Take the radius of the Earth to be 6,378 km.
### (a) Angular Speed Calculation
**Problem:** What is the angular speed (in rad/s) of a point on Earth's surface at latitude 31° N?
**Answer:**
\[ \text{Angular Speed} = 0.0000727 \, \text{rad/s} \]
A green check mark indicates the answer is correct.
### (b) Linear Speed Calculation
**Problem:** What is the linear speed (in m/s) of a point on Earth's surface at latitude 31° N?
**Answer:**
\[ \text{Linear Speed} = 397.45 \, \text{m/s} \]
A green check mark indicates the answer is correct.
### (c) Latitude Calculation for a Given Linear Speed
**Problem:** At what latitude would your linear speed be 32 m/s? (Enter your answer in degrees north of the equator.)
**Answer:**
\[ \text{Latitude} = 76.52° \, \text{N} \]
A red cross indicates the answer is incorrect.
### Explanation of Diagrams
There are no visual diagrams or graphs provided in the text. The calculations are presented in tabular form with individual problem statements and their corresponding answers.
For further understanding, these calculations relate to the Earth's rotation. The angular speed refers to how fast an object moves through an angle (in radians) over time. The linear speed relates to the actual distance an object moves along Earth's surface over time.
**Note:** The incorrect result for the latitude in part (c) suggests a need to either reperform the calculations or analyze the method for any potential errors.
---
This exercise demonstrates important concepts in Earth's rotational dynamics, which can have applications in various scientific fields, such as geography, astronomy, and physics.
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