>I  need to  build a  machine that uses a 1 HP Capacitor start 120v
>electric motor that turns at 3350 rpm. The motor - by way of pulleys -
>will drive a shaft whose rotational speed  should have a controllable
>range from 0 to 200 RPM.

A variable frequency drive motor control will do that.
The newer vector drives will also deliver an almost flat torque curve all
the way down to 5 rpm or so.
They can be programmed for fixed torque or fixed hp.

I have variable frequency drives / phase converters on my milling machine,
drill press, belt grinder etc.
These allow variable speed from 0 rpm to over twice the rated speed on the
nameplate.
VFDs have programmable acceleration and deceleration ramps, sequencing,
reverse, overtorque for starting etc.
Amazing devices.  IGBT inverters have come along way in past few years.

You will need to use a three phase motor to use a VFD, but used these are
cheaper than single phase.
You can get VFDs which have single phase input and 3 phase output.
Mine are 220v single phase input and 220v three phase output.
I have a couple extra VFDs for sale, btw.

Do a newsgroup search for VFD + single phase and that should explain it as
it applies to home use.

Gary Lee
http://www.telusplanet.net/public/gary2a/vw.htm