Dazed in College: Understanding Dimensional Analysis & Metric Units

[chewbocka]

Dazed and Confused!

Help!

Would somebody please explain Dimensional Analysis so that I can understand it...?

And

Is there a standard format to converting Metric Units of Measuring?


Confused in College!

Example:
35mm____________________________m

 

[recon]

1 mm = 0.1 cm

1 cm = 0.01 m
0.1 cm = 0.001 m
So,
1 mm = 0.001 m

35 mm = 35 X 1 mm = 35 X 0.001 m = 0.0035 m

 

[Kelju Ivan]

What Recon meant is that:
35 mm = 35 X 1 mm = 35 X 0.001 m = 0.035 m

One zero too many. .)

Here's a table with the values of different prefixes so you can do the conversions: http://searchsmallbizit.techtarget.com/sDefinition/0,,sid44_gci499008,00.html

Dimensional analysis is used to make sure that the two sides of an equation are comparable, have the same units. We use "general units" to present SI-units. For example, the dimension of length is L and time is T. These can be combined to the dimension of v, which is length per time = L*T^-1.

Usually you need to find out what the exponents of the units need to be for the equation to be consistent.

For example, let's analyze the equation for distance travelled: x = x_0 + vt + ½at^2.

The dimensions are x=L, x_0=L, v=LT^-1, t=T, a=LT^-2 and t^2=T^2.
This gives us the equation L = L + LT^1 * T + LT^-2 * T^2. The right side turns out to be just L:s, so it's dimension is the same as the left side, so it's physically consistent.

Usually you need to find out what the exponents for these units are.

Hope that was clear enough. I'm in a hurry, so I can't write anymore.

 

[kdinser]

The biggest point that my algebra teacher never made, and that the book didn't specifically say, was that all you are really doing in dimensional analysis is multiplying by 1.

Remember that you can multiply anything by 1 and not change it's overall value. (5/7) * (3/3) still has the same value as 5/7 even though it doesn't look exactly the same after you multiply. You could also write it like this and it still means the same thing (5/7) * (3/(1+2)).

In dimensional analysis we do the same thing. If we have 3 miles and we want to go to meters, we set it up so that we multiply by 1 a few times to change the units to meters but the overall value, in this case the distance, stays the same.

start like this
3 miles * (5280 ft/1 mile) * (1 meter/3.28ft) = (15840 miles ft meters)/(3.28 miles ft) = 4829.3 meters

Treat the dimensions (ft, mile, meter) as variables that can be canceled. So in this case, the miles cancel and the ft cancel leaving us with the only units that don't cancel, meters. Divide the top number by the bottom and you get your final answer in meters.

I don't know if this helps or not, but it was the biggest point that I missed the first time I was exposed to it.