I am working on a project which will need an as small as possible DC motor which will spin up to 2500 RPM with a little bit of weight on it, maybe a pound. I don't know a ton about how to pick out the right motor and will need a speed controller too so that I can control this setup with my Arduino. Thanks.

Motor load is a torque, not a weight - you'll have to explain more about the mechanics of the situation or work out the torque yourself. If none of this means anything then just provide more information about the setup please?!

It is for a centrifuge. I am planning on attaching a plastic disc directly to the motor shaft.

It’s aaaaaages since I did this kind of calculation, but the torque T required depends on the Moment of Inertia I of the disk and the required acceleration a, and :

T = Ia

The Moment of Inertia of a disk on mass m and radius r is

I= mr^{2} / 2

(Let’s check those units…

units of I will be kg m^{2}

units of a are rad / s^{2} or just 1/s^{2}

So units of T are kg m^{2} / s^{2}

(Which is right since T=Fd and units of force at kg m / s^{2}) )

I think… it’s been a long time, as I say

I believe you'll want to know the horsepower of the motor.

encryptor: I believe you'll want to know the horsepower of the motor.

Power in Watts is just P = Tw where w (lower case omega) = rotation speed in rads / sec