20050221, 21:19  #1 
Dec 2003
Hopefully Near M48
2·3·293 Posts 
Physics Problem
I'm kind of embarrased to have to ask this here, but I just can't answer this question from my physics homework. I get this feeling that its supposed to be easy:
"What is the linear speed of a point (a) on the Equator, (b) on the Arctic Circle (latitude 66.5 degrees N), (c) at a latitude of 40.0 degrees N, due to the Earth's rotation?" I know how I'm supposed to solve this. I find the circumference of the circle that the point traces in one day, then just divide by 86400 seconds. The problem is, I don't know how to calculate the circumference of the circle. I guess the general way to state my problem is: What is the circumference of a circle drawn around the Earth, parallel to the Equator, at latitude L? I know some boundary conditions: If C(L) represents the circumference at latitude L: C(0) = 2*pi*R C(90) = 0 I also know that C(L) is a strictly decreasing function (this can be seen from the geometric interpretation. As you move closer to the poles, the circles get smaller). That is, if b > a, C(b) < C(a) Also, since the size of the circles change continuous, C(L) is a continuous function. But of course, there are infinitely many functions that satisfy these conditions. Last fiddled with by jinydu on 20050221 at 21:26 
20050221, 21:30  #2  
Banned
"Luigi"
Aug 2002
Team Italia
1001011000000_{2} Posts 
Quote:
I never studied phisics, but if the earth could be considered as a sphere, and R is the radius of the sphere, the radius at latitude x should be R*cosine(x). I'm surely wrong, but I just can't think to a better method... Luigi 

20050221, 21:32  #3  
May 2004
Oslo, Norway
2^{3}·3·5 Posts 
Quote:
regards, Leif. 

20050221, 21:38  #4  
Dec 2003
Hopefully Near M48
2×3×293 Posts 
Quote:
Quote:
Maybe a proof would help here. Thanks Last fiddled with by jinydu on 20050221 at 21:39 

20050221, 21:42  #5 
May 2004
Oslo, Norway
2^{3}·3·5 Posts 
I thougt that we said exactly the same thing. I've got a rule of thumb regarding trigonometrics: Cosine is 1 at 0 degrees, and 0 at 90 degrees. With the sine, it's the opposite.
regards, Leif. 
20050221, 21:59  #6 
Jul 2004
Nowhere
1451_{8} Posts 
here it goes just what to shoot my luck well first you need to find the point from the distence from center of the invisable axis of earth to the radius you kinda could use a model of earth to visualize it find hte point on the same plain get radius then use 3.14(2r)=circumference
r = radius then it would be c/(60*24*365.25)=distence per second /end rambleing i dont know if this can totally work hence being a freshman in highschool but who knows thats what i would do only i would proibily get it wrong gl on it jin 
20050221, 22:11  #7 
Dec 2003
Hopefully Near M48
2×3×293 Posts 
Once I find the radius or circumference of the circle, the rest I can do in my sleep. The problem is getting to that point.
How could I prove mathematically that C(L) = 2pi * R * cos(L) or equivalently r(L) = R * cos(L) Maybe I should have taken a nonEuclidean geometry first? Strangely enough, Mathworld: http://mathworld.wolfram.com/SphericalGeometry.html says that in a sphere, there are no parallel lines. This means that longitude lines intersect?! Last fiddled with by jinydu on 20050221 at 22:14 
20050221, 23:01  #8 
Dec 2003
Hopefully Near M48
2×3×293 Posts 
Please? How do I prove the result?

20050221, 23:04  #9  
Banned
"Luigi"
Aug 2002
Team Italia
2^{6}×3×5^{2} Posts 
Quote:
Luigi Last fiddled with by ET_ on 20050221 at 23:05 

20050221, 23:15  #10  
Banned
"Luigi"
Aug 2002
Team Italia
2^{6}×3×5^{2} Posts 
Quote:
Luigi 

20050222, 01:24  #11 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
9,341 Posts 
Points on the earth don't move in a linear fashion. Even the poles trace out the elipse of the orbit.

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Irish physics  davieddy  Science & Technology  26  20110123 17:03 
Physics problem Please  Joshua2  Homework Help  9  20090302 03:39 
Physics Nobel.  mfgoode  Science & Technology  8  20061013 16:18 
A physics puzzle  hyh1048576  Puzzles  0  20030928 15:14 
Physics Sledding Problem  eepiccolo  Puzzles  10  20030818 19:17 