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As the earth rotates, what is the speed of (a) a physics
Chapter 4, Problem 61P(choose chapter or problem)
Problem 61P
As the earth rotates, what is the speed of (a) a physics student in Miami, Florida, at latitude 26°, and (b) a physics student in Fairbanks, Alaska, at latitude 65°? Ignore the revolution of the earth around the sun. The radius of the earth is 6400 km.
Questions & Answers
QUESTION:
Problem 61P
As the earth rotates, what is the speed of (a) a physics student in Miami, Florida, at latitude 26°, and (b) a physics student in Fairbanks, Alaska, at latitude 65°? Ignore the revolution of the earth around the sun. The radius of the earth is 6400 km.
ANSWER:
Step 1 of 2
(a) We need to find out the speed of the student at a latitude \(26^{0}\).
The velocity of the student is given by,
\(v=r \omega\)
Radius is given by,
\(r=R \cos \omega\)
The radius of the earth, \(R=6400 \mathrm{~km}\)
\(r=6400 \cos 26^{0}\)
\(r=5752.28 \mathrm{~km}\)
Angular velocity is given by;
\(\omega=\frac{\Delta \theta}{\Delta t}=\frac{2 \pi}{24 \times 60 \times 60}\)
\(\omega=7.27 \times 10^{-5} \mathrm{rad} / \mathrm{s}\)
\(v=418.31 \mathrm{~m} / \mathrm{s}\)