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## Some ``Q'' examples

• Q. How fast is a gaucho taking a nap at the equator traveling due to the rotation of the Earth?

Earth Circumference = 24,000 miles [ diameter]

Time for gaucho to make a ``trip around the world'' = 24 hours.

miles/hours

• Q. How fast are we all moving through space due to the Earth's orbit around the Sun?

Distance traveled: miles (diameter of the Earth's orbit)

= 584,600,600 miles miles

Time taken: 1 year hours

Speed miles/hour (!).

• ``Dimensional Analysis''

Note that the ``units'' are important in these equations. They have to work out and they can be used to divine the correct equation to use if your memory or physical reasoning abilities abandon you for some reason. For example:

Q. How fast are we moving through...

Suppose you knew this was somehow related to how far we travel and how long it takes but you can't remember the exact equation. You CAN remember that ``how fast'' must come out in units of velocity like Miles/Hour. So, lets try:

### Speed = Distance traveled x Time taken

The units for the multiplication on the right-hand side are

This can't be right. So, work backwards from the units, the way to end up with the right velocity units is clearly to take the distance traveled divided by the time taken. Then the units are:

Michael Bolte
Wed Jan 14 21:53:00 PST 1998