# About the earths spin

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I found this on a web page and it makes no since to me. if I have a ball and I spin it on the floor, the entire ball is spinning at the same rate of speed. Top Middle an Bottom, still spins the same. How then can the earth spin at different speeds depending on where you are on the planet?

"How fast does the earth spin?

That depends on where on Earth you are standing. At the poles, the Earth hardly spins at all, but as you travel towards the equator, the rotational speed picks up. This makes sense -- as the circumference of a circle increases, a single point along it has to travel faster to complete a revolution in the same amount of time.

The rotational speed of the Earth at the equator is about 1,038 miles per hour. The atmosphere at the equator is also slightly thicker due to rotation, and you weigh slightly less. At mid-latitudes, the speed of the Earth's rotation decreases to 700 to 900 miles per hour. "

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Now I understand this here: " as the circumference of a circle increases, a single point along it has to travel faster to complete a revolution in the same amount of time." But to me this does not explain why this causes some parts of the earth to spin faster than others..

If I imagine this ball with lines coming straight out the ones in the middle will make their revolution longer than the ones at the top But to me this is Not the same as speed. the lines at the top and the lines in the middle are still moving through space at the same rate only traveling a shorter distance. It appears to me this is confusing the issue.

Edited by John Phoenix
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I found this on a web page and it makes no since to me. if I have a ball and I spin it on the floor, the entire ball is spinning at the same rate of speed. Top Middle an Bottom, still spins the same. How then can the earth spin at different speeds depending on where you are on the planet?

"How fast does the earth spin?

That depends on where on Earth you are standing. At the poles, the Earth hardly spins at all, but as you travel towards the equator, the rotational speed picks up. This makes sense -- as the circumference of a circle increases, a single point along it has to travel faster to complete a revolution in the same amount of time.

The rotational speed of the Earth at the equator is about 1,038 miles per hour. The atmosphere at the equator is also slightly thicker due to rotation, and you weigh slightly less. At mid-latitudes, the speed of the Earth's rotation decreases to 700 to 900 miles per hour. "

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Now I understand this here: " as the circumference of a circle increases, a single point along it has to travel faster to complete a revolution in the same amount of time." But to me this does not explain why this causes some parts of the earth to spin faster than others..

If I imagine this ball with lines coming straight out the ones in the middle will make their revolution longer than the ones at the top But to me this is Not the same as speed. the lines at the top and the lines in the middle are still moving through space at the same rate only traveling a shorter distance. It appears to me this is confusing the issue.

So you can picture the Earth's spin clearly, but are struggling with the context of the words used to describe it?

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Imagine a record sitting on a record player. Put a penny on the outside edge and one near the center. The one in the center rotates around in the same time as the one on the outside -- they both go around 33 times per minute, or thereabouts. (Assuming it's an LP.) But speed is the distance traveled divided by the time, and the one on the outside edge travels a far greater distance than the one near the center. So it's going faster.

Just remember: $\mbox{speed} = \frac{\mbox{distance}}{\mbox{time}}$. Time might be the same, but distance is not.

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You and the cited page are talking about different things. You are talking about angular velocity while the web page is talking about plain old vanilla velocity. The two are related via $\vec v = \vec{\omega}\times \vec r$.

Ignoring things like Earth tides, the Earth as a whole is rotating as one. The Earth's angular velocity is one rotation per sidereal day = 23 hours, 56 minutes, 4.091 seconds1. The article was talking about speed, not angular rate. A person standing on the equator is 6,378.137 kilometers from the Earth's rotation axis, and thus is moving at $6378.137\,\text{km}*2\pi/86164.0905\,\text{sec} = 465.101\,\text{m}/\text{s}$. The distance between a person standing at the North Pole and the Earth's rotation axis is zero, so this person's linear velocity is zero.

1 Why not one rotation per 24 hours? The Earth moves in its orbit during that 24 hour period, so the Earth needs to complete a bit more than one full rotation to make the Sun appear to be in the same place from the perspective of a person standing on the Earth.

Edited by swansont
fix LaTex
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There are two types of speed you need to consider when talking about spinning objects.

1) Linear Speed

2) Angular Speed

Linear speed is the speed an object would have if it was let go from the spinning object. Think of weight tied to a piece of string. If you let the string go, the weight would fly off at the Linear Speed it had while you were spinning it around by the string.

The other, Angular speed, is the number of times the object goes around the axis of rotation in a given time. You probably know this form the dashboard in your car. There is a dial that has the letter "RPM" on it. This is the number of times the engine makes a full rotation (360 degrees) in one minute. typically this is around 1000 RPM for an idling engine.

Now for the Earth:

Every point on the Earth makes 1 rotation (360 degrees) in 1 day. So all places on the Earth has the same Angular speed.

However, the Linear speed can be calculated by knowing the Angular speed and the distance the object is from the axis of rotation. The closer something is to the axis of rotation the lower its linear speed for a given angular speed. As places near the north or south pole are close to the axis of rotation are nearer to the axis of rotation of the Earth, then these places have a lower Linear speed (because the angular speed is the same for all places, but the distance form the axis of rotation is not).

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