# Homework Help: Unit Consistency

1. Jul 8, 2009

### jaimieee

Ok, this is not a homework. But we have an exam later 8 hours from now.

On our book there is an activity called the Unit Consistency.

The instruction says: Which of the units below do no exhibit unit consistency? Give the equivalent consistent units for those that are not consistent.

Our Physics teacher gave us some of the consistent units like:

km/h
mi/h
kg/m3

but i'm not sure if only these are the consistent ones, are there still consistent units? Can you share it? Thank you.

2. Jul 8, 2009

### Staff: Mentor

Is there a definition of "consistent units" offered by the book or instructor?

3. Jul 8, 2009

### jaimieee

Yes,yes! Sorry I wasn't able to define.

This is what is EXACTLY written :)

Unit Consistency

whenever you make calculations involving measurements, always remember to check for unit consistency; that is, the units should belong in the same system. Generally, if you are using meter for length, you should use gram for mass. Within the SI, the system of units based on the use of meter and kilogram is referred to as the MKS (meter-kilogram-second) system. Another system is the CGS system, which uses the centimeter, gram and second.

I didn't get it. It's confusing me :(

4. Jul 8, 2009

### mgb_phys

I think they mean which are dimensionally the same.
The basic dimensions are length, mass, time (plus temperature, and current)

So for example speed is length/time so could be given in miles/hour, m/s, km/min furlong/fortnight etc but could never be km/kg
So two sets of units are consistent if they refer to the set of same base units.

5. Jul 8, 2009

### Staff: Mentor

Oh, I understand now. Well, except for the typo in the sentence that says "if you are using meter for length, you should use gram for mass." That is incorrect. As the rest of the paragraph states, the typical unit systems are:

MKS (SI) -- meter, kilogram, second

cgs -- centimeter, gram, second

There are similar consistent unit systems for goofy units like we use here in the US (pounds, whatever). This is a pretty good intro to units, with pointers out to other articles:

http://en.wikipedia.org/wiki/Units_of_measurement

So it looks like the units you posted in your original post (OP) are consistent. Do you see why the following would be inconsistent?

g/m^3

6. Jul 8, 2009

### jaimieee

Hmm for example the given is:
newtons per centimeter , what will be the consistent unit?

I think km/min is not the consistent one? I think it should be km/h? What do you think?

7. Jul 8, 2009

### jaimieee

I kinda get it but i'm not sure if my understanding is correct.

I think the answer should be kg/m^3? I used the MKS (SI).

8. Jul 8, 2009

### Staff: Mentor

Correct. kg/m^3 or g/cm^3 would be consistent sets of units, if I understand the definition correctly.

9. Jul 9, 2009

### vin300

It should be newtons per meter or dynes per centimeter(surface tension)

It is MKS(Meter Kilogram Second) so it is km/s

10. Jul 9, 2009

### jaimieee

Hi. We just had our exam awhile ago but this one was not included. T__T Anyway thank you guys ;)

11. Jul 9, 2009

### Redbelly98

Staff Emeritus
Given the earlier definition, km/s is not consistent by m/s would be.

See Post #1, Item 2 ... km/h is considered to be "consistent units".