I'll need to run power first I guess. So I need to go get a more appropriate power cord, and pig tail to tie the motor and switch all together. I assume the 2 should be the same gauge, but not sure how many conductors I'll need?
Can either if you share the process for figuring that out?
There's not "too" much "process" to figuring that out... Go to the NEC, look up the listed full load amps for a motor of your horsepower, multiply that times 1.25 because motors are awful in how they treat your electrical system, multiply that again by the service factor if it's higher than one, derate for conduits... All sorts of stuff... And from that, figure out the amps you have to wire for. Spoiler- It's 17 amps. I didn't look at your service factor, I called it 1.00. If you have a higher service factor, you won't be using it. Then adjust up if required because (you won't be required, you're already there), but if you had a motor small enough to be "good" on 14gauge or less "behind the walls", you still can't, 12 gauge is the minimum. But that's on a dedicated motor receptacle, or a hard wired motor. You very much can "plug in" a motor to any suitable receptacle/outlet. NEC ends at the outlet.
So, presuming you've verified 12 gauge wire to your outlet that you intend to use- You're good.
NEC does not offer "different minimum standards" for things not covered by it. Assuming you're not using conduit of any type, (From the wall to the lathe, more on that in a second), if you were to apply the NEC's standards for "built in stuff", a 14ga flexible cord is only good for 15 amps. That's fair.
So, from the wall, to the lathe, 17 amps in that cord, when in fact it will NEVER SEE 17 amps sustained- Fiften amps allowable in a 14 gauge cord will do just fine to get power to the lathe, presuming the length is reasonable. If it's gonna be a fifteen or twenty foot cord, then consider 12 gauge. It'll more'n likely work anyhow with 14 gauge, but you're already nearing a capacity before the cord gets long, 12 would be better and warranted in that case. But under 25 feet or so, no lectures from me on burning the house down on that particular aspect.
Then, from the switch to the motor- Absolutely 14 gauge is fine for that. The run is gonna be well under two feet, and even though there are conduit derate rules and such- You're inherently going tho have equal current in all the wires, the run is short, well below the "nipple rule" for conduit fill, there's ten thousand exceptions for motor hookups that let you do things differently than other electrical installations. Basically, whatever conduit you choose to contain the wires, it's got to hold your "switch to motor" bundle inside of it, but you can literally stuff it as full as you want (you can NOT stuff enough insulated wires into a conduit to violate the code, so no worries about doing the same in a pllace that falls outside the code... Any conduit you like, 14 gauge wires, and while on that short of a run, 16 gauge "could do it", and it would work, it'd be brutal. The cost difference from one to the next rounds to about nothing. So 14 gauge there for sure.
So from all of that, I'm calling out 14 gauge for everything, UNLESS the power cord lengths gets excessive.
How's that for how I got there. I really wish that NEC was made public. It's paid access. You don't need it for a job this small. They keep it under TIGHT copyrite wraps, as purchasing that book is what funds the making of that book. I'd like to have put up snips. I don't like it that way, but there it is...
Anyhow....
The power cord from the wall, you could make that up, or it may or may not be socially acceptable in your neck of the woods to cut up a14 gauge extension cord, liberate it from it's female end, strip back the jacket, and there you go. (That's not right... If you tell anybody Isaid that, I'll deny it). Or make one up out of some service cord (SJOOW would be nice), and then you'd have an industrial cord that you could walk on and drive cars over and such... That's real money though. Only if it's needed.
Conduit. You could absolutely use J cord again. Not conduit but I'm lumping it in anyhow because it's well protected wiring.
Here's a couple of common things to see what you can comes easily over there on the other side of the country from where I shop. All are fine options,
Cord (proper flexible cord that is NOT an extension cord). is the easiest option IF short lengths are available easily to you. And I perefer that, but it's pretty much cosmetic, they're all fine..
MC cable (the flexible metal cable type wiring with wires pre-installed. It's a bear to strip unless you buy a tool)
FMC conduit (the metal jacket like above, except stuff your own wires)
Liquid tight conduit (Very popular, takes special box connectors). is a popular choice.
The loose wire you want for anything that does not come with wires in it is 14 gauge THHN. Or there may or may not be 14 gauge stranded wire left over inside the other half of the extension cord that you may or may not have cut up to make the power cord. (That's not right... If you tell anybody Isaid that, I'll deny this too.)
All of those are gonna need two suitable connectors, one at the switch and one at the motor.
