Homogeneity of Equations
Most recent answer: 10/21/2010
Q:
2 days ago, we were taught what does the homogeneity of an equation mean (all terms in a homogeneous equation have the same combination of SI base units); we were also told that homogeneous equations are not always Physically/scientifically correct:eg. E=1/2mv2 and E=mv2
So,what is the use/purpose of finding whether the equation is homogeneous or not??!
Thanks in advance.
- Anonynous (age 16)
- Anonynous (age 16)
A:
I wasn't familiar with this term, but it closely resembles something we do try to teach. In order for an equation to be correct, the two sides have to have the same dimensions. For example, you can't have a weight being equal to a length. It just wouldn't make any sense.
Often, in working through the algebra to get some physical equation we make some mistake. If when you're done you see that the dimensions on the two sides are different, then you know right away that there was a goof. It's a very easy check that probably catches a majority of errors.
Of course, as you point out, having the right dimensions doesn't guarantee that the equation is right. Having the wrong ones does guarantee it's wrong.
Once you've got the basic dimensions right, if you want to plug in numerical values you have to make sure that the units are the same on both sides. You wouldn't want to express one side in inches and the other in meters, which would mess up the numerical equality. Sticking to SI units is one way to take care of that.
Mike W.
Often, in working through the algebra to get some physical equation we make some mistake. If when you're done you see that the dimensions on the two sides are different, then you know right away that there was a goof. It's a very easy check that probably catches a majority of errors.
Of course, as you point out, having the right dimensions doesn't guarantee that the equation is right. Having the wrong ones does guarantee it's wrong.
Once you've got the basic dimensions right, if you want to plug in numerical values you have to make sure that the units are the same on both sides. You wouldn't want to express one side in inches and the other in meters, which would mess up the numerical equality. Sticking to SI units is one way to take care of that.
Mike W.
(published on 10/21/2010)