What variable doesn't have a unit?

augmented reality

Is there any values which don't have an SI or any unit.
Speed=ms-1
Mass=grams etc.
Is there any variable which is just a number, no unit after?

Professor_Fink

If you're a theoretical physicist, nothing has a unit. You can non-dimensionalise everything. We usually simpy set c=1, hbar=1, etc...

FISMA

augmented reality wrote: »

Is there any values which don't have an SI or any unit.
Speed=ms-1
Mass=grams etc.
Is there any variable which is just a number, no unit after?

There are a few quantities that do not have units.

Anytime you have a ratio, units divide out. Hence, coefficients, such as that for static or Kinetic Friction are unitless.

The proper way to measure angles are with radians, which are essentially unitless.

DailyBlaa

Refractive Index and Reynolds Number are the first two that popped into my head. There are lots more here.

thecatspjs

Anytime you have a ratio, units divide out. Hence, coefficients, such as that for static or Kinetic Friction are unitless.

The proper way to measure angles are with radians, which are essentially unitless.

Aren't radians units themselves?? Also, kinetic friction is a constant, not a variable. Not trying to be a bollox or anything!

ZRelation

thecatspjs wrote: »

Aren't radians units themselves?? Also, kinetic friction is a constant, not a variable. Not trying to be a bollox or anything!

Yes radians are a unit themselves, albeit a derived unit, like Newtons. In the general case the kinetic friction coefficient isn't necessarily constant and can depend on temperature, slip rate and applied pressure in a system.

FISMA

A radian is a pure number - no units.

The definition of a radian is a ratio. length/length - no units

The angle subtended by an arc length that is equal to the radius of the circle is one radian.

θ = s/r

The problem usually does not arise in Maths class where they would rarely use rads.

However, in Physics where we are studying the natural world via measurements, we use units. Thus, Physics teachers say things like there are 2π rads in a circle. Many students incorrectly take this to mean that the "rads" bit is a unit when it is not. "rads" may be omitted.

ZRelation wrote: »

..., albeit a derived unit, like Newtons.

I would be careful here. A Newton, in SI base units is a kg*m/s^2. What are the SI base units of the radian?

Also, if you disagree that θ has units, then what are the units of Pi (π)? Given that

C = 2πr => π = C/2r -> m/m = 1
or
A = πr^2 => π = A/r^2 -> m^2/m^2 = 1

You may define a fictitious unit. But understand what you are doing.

ZRelation

Ok well as far as I can see the radian is classified as one of 22 derived SI units http://physics.nist.gov/cuu/Units/units.html , along with Newtons. When expressed in terms of SI base units you get 1, from m.m-1, which makes sense to me.

This '1' is often omitted, which agrees with what you were saying when you stated that the term 'rads' could be theoretcially omitted (although to do so leads to confusion in terms of angular measure used.)

The symbol rad or radians is used to describe the unit in the same way N or Newton is used to described that particular derived unit, so I would argue that the use of rad is as legitimate as the use of Newton in symbolizing the unit.

O f course there are other (fictitious) dimensionless units out there, such as microstrain(used alot in engineering) http://www.omega.com/literature/transactions/volume3/strain.html, which aren't SI.