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 October 20th, 2007, 10:54 AM #1 Newbie   Joined: Oct 2007 Posts: 19 Thanks: 0 Degrees and Radians The earth rotates on its axis once every 24 hours. a)How long does it take earth to rotate through an angle of 4pi/3? b)how long does it take earth to rotate through an angle of 120 degree?
 October 20th, 2007, 11:32 AM #2 Senior Member   Joined: Dec 2006 Posts: 1,111 Thanks: 0 There are 360 degrees and 2*pi radians in a complete revolution. Does that help? Just find the ratio between the angle being traveled by the Earth in the problem and the number of degrees/radians in a full revolution, and then multiply that by the amount of time it takes the Earth to rotate around its axis.
 October 21st, 2007, 02:47 PM #4 Global Moderator   Joined: May 2007 Posts: 6,558 Thanks: 602 Slight nitpicking. The earth takes slightly less (I think about 4 min.) than 24 hours to rotate 360 deg. The extra time is needed to complete an earth day because the earth has moved 1/365th of its distance in orbit around the sun.
 October 21st, 2007, 04:32 PM #5 Senior Member   Joined: Dec 2006 Posts: 1,111 Thanks: 0 I can't see how motion around the sun influences the length of the day. If we define a point that the Earth starts from and ends from in regards to spinning motion, moving around the Sun shouldn't influence that (I think).
October 21st, 2007, 06:25 PM   #6
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Quote:
 Originally Posted by Infinity I can't see how motion around the sun influences the length of the day.
If you had permanent day, the rotation rate would be one rotation per year, wouldn't it?

October 21st, 2007, 07:08 PM   #7
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Quote:
 I can't see how motion around the sun influences the length of the day.
OK, so you are defining the day as how much time we get sunlight. I am defining it as how long it takes the Earth to spin once (360 degrees) on its axis.

Quote:
 If you had permanent day, the rotation rate would be one rotation per year, wouldn't it?
Yes, similar to the moon going around the Earth.

October 22nd, 2007, 01:48 PM   #8
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Quote:
 Originally Posted by Infinity I can't see how motion around the sun influences the length of the day. If we define a point that the Earth starts from and ends from in regards to spinning motion, moving around the Sun shouldn't influence that (I think).
A day is defined in terms of how the earth is facing the sun, that is from noon to noon, where noon is defined as the time that the sun is directly overhead (at the appropriate latitude). Since the earth has moved in its orbit, it has to rotate more than 360 deg. to get there.

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# through how many radians does the earth turn in 1 hour

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